Question 1

Let $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ be a universal set and $A = \{1, 3, 5, 7, 9\}$. What is the complement of set $A$, denoted as $A'$?

Accepted Answer

Correct Option: A. Solution: The complement of a set $A$ in a universal set $U$ is the set of elements in $U$ that are not in $A$. Therefore, $A' = \{2, 4, 6, 8, 10\}$.

Question 2

Consider the sets $A = \{2, 4, 6, 8\}$ and $B = \{6, 8, 10, 12\}$. If $C = A \cup B$, which of the following statements is true?

Accepted Answer

Correct Option: A. Solution: The union of sets $A$ and $B$ is the set of all elements that are in either $A$ or $B$, or both. Therefore, $C = A \cup B = \{2, 4, 6, 8, 10, 12\}$.

Question 3

Given $A = \{2, 4, 6, 8\}$ and $B = \{6, 8, 10, 12\}$, what is $A \cap B$?

Accepted Answer

Correct Option: B. Solution: The intersection of sets $A$ and $B$ is the set of elements that are common to both $A$ and $B$. Thus, $A \cap B = \{6, 8\}$.

Question 4

Who is credited with the development of the modern theory of sets?

Accepted Answer

Correct Option: B. Solution: Georg Cantor is credited with the development of the modern theory of sets, as he published papers on set theory between 1874 and 1897.

Question 5

Which of the following statements is true regarding the sets $A = \{2, 4, 6, 8\}$ and $B = \{1, 3, 5, 7\}$?

Accepted Answer

Correct Option: B. Solution: Two sets are disjoint if they have no elements in common. Here, $A$ and $B$ have no common elements, so they are disjoint sets.

Question 6

Consider the sets $A = \{1, 2, 3, 4, 5\}$ and $B = \{3, 4, 5, 6, 7\}$. If $C = A \cap B$, which of the following statements is true about the set $C$?

Accepted Answer

Correct Option: A. Solution: The intersection of sets $A$ and $B$, denoted as $A \cap B$, is the set of elements common to both $A$ and $B$. Therefore, $C = \{3, 4, 5\}$, which is a subset of both $A$ and $B$.

Question 7

Which of the following intervals is a closed interval?

Accepted Answer

Correct Option: D. Solution: A closed interval $[a, b]$ includes both endpoints $a$ and $b$.

Question 8

If $A = \{1, 2, 3, 4, 5, 6\}$ and $B = \{2, 4, 6, 8\}$, what is $A - B$?

Accepted Answer

Correct Option: A. Solution: $A - B$ is the set of elements that are in $A$ but not in $B$, which are $\{1, 3, 5\}$.

Question 9

Which mathematician criticized Cantor's treatment of infinite sets as being similar to finite sets, leading to a significant debate in the mathematical community?

Accepted Answer

Correct Option: C. Solution: Leopold Kronecker criticized Cantor for treating infinite sets in the same way as finite sets, which was a point of contention in the development of set theory.

Question 10

Let $U$ be the universal set and $A = \{a, e, i, o, u\}$ be a subset of $U$. If $A'$ denotes the complement of $A$, which of the following statements is true?

Accepted Answer

Correct Option: C. Solution: The complement of a set $A$ with respect to a universal set $U$ is the set of all elements in $U$ that are not in $A$. Thus, $A' = \{x : x \in U 	ext{ and } x 
otin A\}$.

Question 11

Convert the set $B = \{x : x 	ext{ is a prime number less than 10}\}$ into roster form.

Accepted Answer

Correct Option: A. Solution: The prime numbers less than 10 are 2, 3, 5, and 7. Hence, the roster form is {2, 3, 5, 7}.

Question 12

If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ is the universal set and $A = \{2, 4, 6, 8\}$, what is the complement of $A$?

Accepted Answer

Correct Option: A. Solution: The complement of $A$ consists of all elements in $U$ that are not in $A$. Thus, $A' = \{1, 3, 5, 7, 9\}$.

Question 13

If $U$ is the universal set and $A = \{2, 3\}$, $B = \{3, 4, 5\}$, what is $A' \cap B'$?

Accepted Answer

Correct Option: A. Solution: The complement of $A$ is $A' = \{1, 4, 5, 6\}$ and the complement of $B$ is $B' = \{1, 2, 6\}$. Therefore, $A' \cap B' = \{1, 6\}$.

Question 14

Convert the set $$A = \{x : x 	ext{ is a natural number and } 3 < x < 10\}$$ into roster form.

Accepted Answer

Correct Option: B. Solution: The set-builder form $$A = \{x : x 	ext{ is a natural number and } 3 < x < 10\}$$ translates to the roster form {4, 5, 6, 7, 8, 9}.

Question 15

Given the universal set $U = \{1, 2, 3, 4, 5, 6\}$, $A = \{2, 3\}$, and $B = \{3, 4, 5\}$, find $(A \cup B)'$.

Accepted Answer

Correct Option: A. Solution: The union $A \cup B = \{2, 3, 4, 5\}$. The complement $(A \cup B)'$ is the set of all elements in $U$ that are not in $A \cup B$, which is $\{1, 6\}$.

Question 16

Georg Cantor is credited with the development of set theory. Which of the following statements best describes his contribution to mathematics?

Accepted Answer

Correct Option: C. Solution: Georg Cantor first encountered sets while working on problems related to trigonometric series, which led to the development of set theory.

Question 17

What is the union of sets $A = \{2, 4, 6, 8\}$ and $B = \{6, 8, 10, 12\}$?

Accepted Answer

Correct Option: A. Solution: The union of two sets $A$ and $B$ is the set of all elements that are in either $A$ or $B$, or in both. Thus, $A \cup B = \{2, 4, 6, 8, 10, 12\}$.

Question 18

Consider the sets $A = \{x : x 	ext{ is a natural number and } 1 < x \leq 6\}$ and $B = \{x : x 	ext{ is a natural number and } 6 < x < 10\}$. What is the union $A \cup B$?

Accepted Answer

Correct Option: B. Solution: The union of sets $A$ and $B$ includes all elements that are in either $A$ or $B$. Therefore, $A \cup B = \{2, 3, 4, 5, 6, 7, 8, 9\}$.

Question 19

Given the universal set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and a subset $A = \{1, 3, 5, 7, 9\}$, what is $A'$?

Accepted Answer

Correct Option: A. Solution: The complement $A'$ consists of all elements in $U$ that are not in $A$. Therefore, $A' = \{2, 4, 6, 8, 10\}$.

Question 20

Given the sets $A = \{a, e, i, o, u\}$ and $B = \{a, i, u\}$, what is $A \cap B$?

Accepted Answer

Correct Option: B. Solution: The intersection $A \cap B$ is the set of elements that are common to both $A$ and $B$. Thus, $A \cap B = \{a, i, u\}$.

Question 21

The development of axiomatic set theory was a response to various paradoxes. Which of the following axiomatizations was introduced by John Von Neumann?

Accepted Answer

Correct Option: B. Solution: John Von Neumann introduced the axiom of regularity and contributed to the Von Neumann-Bernays set theory.

Question 22

Which of the following statements is true about the set operation of union?

Accepted Answer

Correct Option: A. Solution: The union of two sets $A$ and $B$ is commutative, meaning $A \cup B = B \cup A$.

Question 23

In a Venn diagram, which of the following represents the union of two sets $A$ and $B$?

Accepted Answer

Correct Option: B. Solution: The union of two sets $A$ and $B$ is represented by the area that includes all elements that are in $A$, in $B$, or in both.

Question 24

Which of the following statements is true regarding the historical development of set theory?

Accepted Answer

Correct Option: B. Solution: The assumption of the existence of a set of all sets led to Russell's Paradox, which was shown by Bertrand Russell in 1902.

Question 25

Consider the sets $A = \{1, 2, 3, 4, 5\}$ and $B = \{3, 4, 5, 6, 7\}$. What is the result of the operation $A \cap B$?

Accepted Answer

Correct Option: B. Solution: The intersection of sets $A$ and $B$ includes elements common to both sets, which are $3, 4, 5$. Thus, $A \cap B = \{3, 4, 5\}$.

Question 26

Which of the following is an example of a set operation that is not commutative?

Accepted Answer

Correct Option: C. Solution: The difference of sets $A - B$ is not necessarily equal to $B - A$, making it non-commutative.

Question 27

Consider the sets $A = \{1, 2, 3, 4, 5, 6\}$ and $B = \{2, 4, 6, 8\}$. What is the result of the operation $A - B$?

Accepted Answer

Correct Option: A. Solution: The set $A - B$ consists of elements that are in $A$ but not in $B$. Thus, $A - B = \{1, 3, 5\}$.

Question 28

Consider the sets $A = \{2, 3, 5\}$ and $B = \{3, 5, 7\}$. According to De Morgan's Laws, what is the complement of the union of $A$ and $B$ with respect to the universal set $U = \{1, 2, 3, 4, 5, 6, 7\}$?

Accepted Answer

Correct Option: A. Solution: The union of $A$ and $B$ is $A \cup B = \{2, 3, 5, 7\}$. The complement of $A \cup B$ with respect to $U$ is $U - (A \cup B) = \{1, 4, 6\}$.

Question 29

If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and $A = \{1, 3, 5, 7, 9\}$, what is the complement of $A$ with respect to $U$?

Accepted Answer

Correct Option: B. Solution: The complement of $A$ with respect to $U$ consists of all elements in $U$ that are not in $A$. Thus, $A' = \{2, 4, 6, 8, 10\}$.

Question 30

If $A = \{a, e, i, o, u\}$ and $B = \{a, i, u\}$, what is the result of the union $A \cup B$?

Accepted Answer

Correct Option: A. Solution: The union of two sets $A$ and $B$ is the set of all elements that are in $A$, in $B$, or in both. Thus, $A \cup B = \{a, e, i, o, u\}$.

Question 31

Given sets $A = \{2, 3, 5\}$ and $B = \{3, 4, 5, 6\}$, what is $A \cap B$?

Accepted Answer

Correct Option: B. Solution: The intersection $A \cap B$ consists of elements common to both sets, which are $\{3, 5\}$.

Question 32

Identify the error in the following statement: The set $$\{x : x 	ext{ is a natural number and } x^2 < 40\}$$ is represented in roster form as {1, 2, 3, 4, 5, 6, 7}.

Accepted Answer

Correct Option: C. Solution: The correct roster form for the set $$\{x : x 	ext{ is a natural number and } x^2 < 40\}$$ is {1, 2, 3, 4, 5, 6}, excluding 7, as $7^2 = 49$ which is not less than 40.

Question 33

Consider the set $A = \{x : x 	ext{ is a natural number and } x^2 < 20\}$. Which of the following represents this set in roster form?

Accepted Answer

Correct Option: A. Solution: The set $A = \{x : x 	ext{ is a natural number and } x^2 < 20\}$ includes numbers whose squares are less than 20. These numbers are 1, 2, 3, and 4.

Question 34

Which of the following sets is an example of an empty set?

Accepted Answer

Correct Option: A. Solution: The set of odd natural numbers divisible by 2 is empty because no odd number can be divisible by 2.

Question 35

Which of the following set-builder forms correctly represents the set $C = \{4, 8, 12, 16\}$?

Accepted Answer

Correct Option: A. Solution: The set $C = \{4, 8, 12, 16\}$ includes multiples of 4 starting from 4 up to 16. Thus, the correct set-builder form is {x : x 	ext{ is a multiple of 4 and } 4 \leq x \leq 16}.

Question 36

If $A = \{x : x 	ext{ is a natural number and } 1 < x \leq 5\}$ and $B = \{x : x 	ext{ is a natural number and } 3 \leq x < 7\}$, what is $(A \cap B)'$ with respect to the universal set $U = \{1, 2, 3, 4, 5, 6, 7\}$?

Accepted Answer

Correct Option: A. Solution: The intersection $A \cap B = \{3, 4, 5\}$. The complement $(A \cap B)'$ with respect to $U$ is $U - (A \cap B) = \{1, 2, 6, 7\}$.

Question 37

Which of the following statements about the intersection of sets is true?

Accepted Answer

Correct Option: B. Solution: The intersection of two sets $A$ and $B$ is defined as the set of all elements that are common to both $A$ and $B$.

Question 38

If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, $A = \{1, 2, 3, 4\}$, and $B = \{2, 4, 6, 8\}$, what is $(A \cup B)'$?

Accepted Answer

Correct Option: A. Solution: The union $A \cup B = \{1, 2, 3, 4, 6, 8\}$. The complement of this set with respect to $U$ is $\{5, 7, 9\}$.

Question 39

Given the sets $A = \{2, 4, 6, 8\}$ and $B = \{1, 3, 5, 7\}$, which statement is correct?

Accepted Answer

Correct Option: B. Solution: Sets $A$ and $B$ are disjoint, meaning they have no elements in common, so $A \cap B = \emptyset$.

Question 40

If $A = \{x : x 	ext{ is a natural number and } 1 < x \leq 5\}$ and $B = \{x : x 	ext{ is a natural number and } 3 < x \leq 7\}$, what is $A \cup B$?

Accepted Answer

Correct Option: A. Solution: The union $A \cup B$ includes all elements from both sets: $\{2, 3, 4, 5, 6, 7\}$.

Question 41

If $A = \{1, 2, 3\}$ and $B = \{2, 3, 4\}$, what is the intersection $A \cap B$?

Accepted Answer

Correct Option: B. Solution: The intersection $A \cap B$ includes elements common to both sets, which are $2$ and $3$.

Question 42

According to De Morgan's laws, what is the complement of the union of two sets $A$ and $B$?

Accepted Answer

Correct Option: A. Solution: De Morgan's laws state that the complement of the union of two sets $A$ and $B$ is the intersection of their complements: $(A \cup B)' = A' \cap B'$.

Question 43

Given the sets $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$, what is the intersection $A \cap B$?

Accepted Answer

Correct Option: B. Solution: The intersection of two sets $A$ and $B$ is the set of all elements that are common to both $A$ and $B$. Thus, $A \cap B = \{3, 4\}$.

Question 44

In a Venn diagram, if $A$ and $B$ are disjoint sets, what is $A \cap B$?

Accepted Answer

Correct Option: B. Solution: Disjoint sets have no elements in common, so $A \cap B = \Phi$.

Question 45

What is the complement of a set $A$ with respect to a universal set $U$?

Accepted Answer

Correct Option: A. Solution: The complement of a set $A$ with respect to a universal set $U$ is the set of all elements in $U$ that are not in $A$, denoted as $A' = \{ x : x \in U 	ext{ and } x 
otin A \}$.

Question 46

If $A = \{x : x 	ext{ is a natural number and } x^2 \leq 4\}$ and $B = \{x : x 	ext{ is a prime number less than 3\}}$, what is $A \cap B$?

Accepted Answer

Correct Option: B. Solution: The set $A = \{1, 2\}$ and $B = \{2\}$. The intersection $A \cap B = \{2\}$.

Question 47

If $A = \{2, 4, 6, 8\}$ and $B = \{4, 6\}$, what does the Venn diagram illustrate about the relationship between $A$ and $B$?

Accepted Answer

Correct Option: B. Solution: In the Venn diagram, $B$ is entirely contained within $A$, indicating that $B$ is a subset of $A$.

Question 48

Which of the following is a subset of the set of real numbers $R$?

Accepted Answer

Correct Option: D. Solution: All these sets, $N$, $Z$, and $Q$, are subsets of the set of real numbers $R$.

Question 49

If $U = \{a, b, c, d, e, f, g, h\}$ is a universal set and $A = \{a, b, c\}$, what is $A'$?

Accepted Answer

Correct Option: A. Solution: The complement of $A$ with respect to $U$ is the set of all elements in $U$ that are not in $A$. Thus, $A' = \{d, e, f, g, h\}$.

Question 50

Using De Morgan's Laws, find the complement of the intersection of sets $A = \{1, 2, 3\}$ and $B = \{3, 4, 5\}$ with respect to the universal set $U = \{1, 2, 3, 4, 5, 6\}$.

Accepted Answer

Correct Option: A. Solution: The intersection $A \cap B = \{3\}$. The complement $(A \cap B)'$ with respect to $U$ is $U - (A \cap B) = \{1, 2, 4, 5, 6\}$.

Question 51

Which of the following sets is represented in set-builder form as $$\{x : x 	ext{ is a vowel in the English alphabet}\}$$?

Accepted Answer

Correct Option: A. Solution: The set-builder form $$\{x : x 	ext{ is a vowel in the English alphabet}\}$$ corresponds to the roster form {a, e, i, o, u}.

Question 52

Let $A = \{1, 2, 3, 4, 5, 6\}$ and $B = \{2, 4, 6, 8\}$. What is the set $A - B$?

Accepted Answer

Correct Option: A. Solution: The set $A - B$ consists of elements in $A$ that are not in $B$. Thus, $A - B = \{1, 3, 5\}$.

Question 53

If $A$ and $B$ are subsets of a universal set $U$, which of the following represents the complement of the union of $A$ and $B$?

Accepted Answer

Correct Option: A. Solution: According to De Morgan's laws, the complement of the union of two sets $A$ and $B$ is the intersection of their complements: $(A \cup B)' = A' \cap B'$.

Question 54

In a Venn diagram, if set $A = \{2, 4, 6, 8\}$ and set $B = \{4, 6, 8, 10\}$, what does the shaded region representing $A - B$ contain?

Accepted Answer

Correct Option: A. Solution: The set difference $A - B$ contains elements that are in $A$ but not in $B$. Here, $2$ is the only element in $A$ that is not in $B$, so $A - B = \{2\}$.

Question 55

Which of the following statements correctly represents the intersection of two sets $A$ and $B$?

Accepted Answer

Correct Option: B. Solution: The intersection of two sets $A$ and $B$ is the set of all elements which belong to both $A$ and $B$: $A \cap B = \{x : x \in A 	ext{ and } x \in B\}$.

Question 56

Given the set $D = \{x : x 	ext{ is a letter in the word 'MATHEMATICS'}\}$, which of the following is the correct roster form?

Accepted Answer

Correct Option: A. Solution: The set $D = \{x : x 	ext{ is a letter in the word 'MATHEMATICS'}\}$ includes all distinct letters in the word, which are M, A, T, H, E, I, C, and S.

Question 57

Given the sets $A = \{x : x 	ext{ is an even natural number}\}$ and $B = \{x : x 	ext{ is an odd natural number}\}$, which of the following statements is true about $A$ and $B$?

Accepted Answer

Correct Option: A. Solution: Sets $A$ and $B$ are disjoint, so $A \cap B = \{\}$. Their union $A \cup B$ is the set of all natural numbers.

Question 58

Let $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ be the universal set and $A = \{1, 2, 3, 4\}$, $B = \{2, 4, 6, 8\}$. What is the complement of the intersection $A \cap B$?

Accepted Answer

Correct Option: B. Solution: The intersection $A \cap B = \{2, 4\}$. The complement of this intersection with respect to $U$ is $U - (A \cap B) = \{1, 3, 5, 6, 7, 8, 9\}$.

Question 59

The set of real numbers $R$ can be fully described in roster form.

Accepted Answer

Answer: False. Solution: The set of real numbers cannot be fully described in roster form because it does not follow a particular pattern and contains infinitely many elements.

Question 60

The intersection of two sets A and B is the set of all elements that are either in A or in B.

Accepted Answer

Answer: False. Solution: The intersection of two sets A and B is the set of all elements that are common to both A and B, not elements that are either in A or B.

Question 61

An open interval $(a, b)$ includes its endpoints $a$ and $b$.

Accepted Answer

Answer: False. Solution: An open interval $(a, b)$ does not include its endpoints $a$ and $b$. It includes all the points between $a$ and $b$ but not the endpoints themselves.

Question 62

The complement of a set $A$ within a universal set $U$ is represented as $A' = U - A$.

Accepted Answer

Answer: True. Solution: The complement of a set $A$ within a universal set $U$ is indeed represented as $A' = U - A$, which includes all elements in $U$ that are not in $A$. This is a fundamental property of set complements.

Question 63

In roster form, the order of elements in a set is important.

Accepted Answer

Answer: False. Solution: In roster form, the order in which the elements are listed is immaterial.

Question 64

The complement of the union of two sets is equal to the intersection of their complements, according to De Morgan's laws.

Accepted Answer

Answer: True. Solution: De Morgan's laws state that the complement of the union of two sets $A$ and $B$ is equal to the intersection of their complements, i.e., $(A \cup B)' = A' \cap B'$. This law is fundamental in set theory.

Sets

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Set Theory Fundamentals

Union and Intersection of Sets

Difference and Complement of Sets

Venn Diagrams

Subsets and Intervals

De Morgan's Laws

Historical Development of Set Theory

Set Representation: Roster and Set-Builder Form

Universal Set and Set Complements

Cardinality and Practical Set Problems

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Set Theory Fundamentals

Union and Intersection of Sets

Difference and Complement of Sets

Venn Diagrams

Subsets and Intervals

De Morgan's Laws

Set Representation: Roster and Set-Builder Form

Universal Set and Set Complements

Cardinality and Practical Set Problems

Exam Tips

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Multiple Choice Questions

Q1.Let U={1,2,3,4,5,6,7,8,9,10}U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}U={1,2,3,4,5,6,7,8,9,10} be a universal set and A={1,3,5,7,9}A = \{1, 3, 5, 7, 9\}A={1,3,5,7,9}. What is the complement of set AAA, denoted as A′A'A′?

Correct Answer: A

Q2.Consider the sets A={2,4,6,8}A = \{2, 4, 6, 8\}A={2,4,6,8} and B={6,8,10,12}B = \{6, 8, 10, 12\}B={6,8,10,12}. If C=A∪BC = A \cup BC=A∪B, which of the following statements is true?

Correct Answer: A

Q3.Given A={2,4,6,8}A = \{2, 4, 6, 8\}A={2,4,6,8} and B={6,8,10,12}B = \{6, 8, 10, 12\}B={6,8,10,12}, what is A∩BA \cap BA∩B?

Correct Answer: B

Q4.Who is credited with the development of the modern theory of sets?

Correct Answer: B

Q5.Which of the following statements is true regarding the sets A={2,4,6,8}A = \{2, 4, 6, 8\}A={2,4,6,8} and B={1,3,5,7}B = \{1, 3, 5, 7\}B={1,3,5,7}?

Correct Answer: B

Q6.Consider the sets A={1,2,3,4,5}A = \{1, 2, 3, 4, 5\}A={1,2,3,4,5} and B={3,4,5,6,7}B = \{3, 4, 5, 6, 7\}B={3,4,5,6,7}. If C=A∩BC = A \cap BC=A∩B, which of the following statements is true about the set CCC?

Correct Answer: A

Q7.Which of the following intervals is a closed interval?

Correct Answer: D

Q8.If A={1,2,3,4,5,6}A = \{1, 2, 3, 4, 5, 6\}A={1,2,3,4,5,6} and B={2,4,6,8}B = \{2, 4, 6, 8\}B={2,4,6,8}, what is A−BA - BA−B?

Correct Answer: A

Q9.Which mathematician criticized Cantor's treatment of infinite sets as being similar to finite sets, leading to a significant debate in the mathematical community?

Correct Answer: C

Q10.Let UUU be the universal set and A={a,e,i,o,u}A = \{a, e, i, o, u\}A={a,e,i,o,u} be a subset of UUU. If A′A'A′ denotes the complement of AAA, which of the following statements is true?

Correct Answer: C

Q11.Convert the set B={x:x is a prime number less than 10}B = \{x : x \text{ is a prime number less than 10}\}B={x:x is a prime number less than 10} into roster form.

Correct Answer: A

Q12.If U={1,2,3,4,5,6,7,8,9}U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}U={1,2,3,4,5,6,7,8,9} is the universal set and A={2,4,6,8}A = \{2, 4, 6, 8\}A={2,4,6,8}, what is the complement of AAA?

Correct Answer: A

Q13.If UUU is the universal set and A={2,3}A = \{2, 3\}A={2,3}, B={3,4,5}B = \{3, 4, 5\}B={3,4,5}, what is A′∩B′A' \cap B'A′∩B′?

Correct Answer: A

Q14.Convert the set A={x:x is a natural number and 3<x<10}A = \{x : x \text{ is a natural number and } 3 < x < 10\}A={x:x is a natural number and 3<x<10} into roster form.

Correct Answer: B

Q15.Given the universal set U={1,2,3,4,5,6}U = \{1, 2, 3, 4, 5, 6\}U={1,2,3,4,5,6}, A={2,3}A = \{2, 3\}A={2,3}, and B={3,4,5}B = \{3, 4, 5\}B={3,4,5}, find (A∪B)′(A \cup B)'(A∪B)′.

Correct Answer: A

Q16.Georg Cantor is credited with the development of set theory. Which of the following statements best describes his contribution to mathematics?

Correct Answer: C

Q17.What is the union of sets A={2,4,6,8}A = \{2, 4, 6, 8\}A={2,4,6,8} and B={6,8,10,12}B = \{6, 8, 10, 12\}B={6,8,10,12}?

Correct Answer: A

Correct Answer: B

Q19.Given the universal set U={1,2,3,4,5,6,7,8,9,10}U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}U={1,2,3,4,5,6,7,8,9,10} and a subset A={1,3,5,7,9}A = \{1, 3, 5, 7, 9\}A={1,3,5,7,9}, what is A′A'A′?

Correct Answer: A

Q20.Given the sets A={a,e,i,o,u}A = \{a, e, i, o, u\}A={a,e,i,o,u} and B={a,i,u}B = \{a, i, u\}B={a,i,u}, what is A∩BA \cap BA∩B?

Correct Answer: B

Q21.The development of axiomatic set theory was a response to various paradoxes. Which of the following axiomatizations was introduced by John Von Neumann?

Correct Answer: B

Q22.Which of the following statements is true about the set operation of union?

Correct Answer: A

Q23.In a Venn diagram, which of the following represents the union of two sets AAA and BBB?

Correct Answer: B