This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Equal Sets”.

1. Which of the following two sets equal?

a) {1,2,3} and {2,3,4}

b) {1,3,5} and {1,3,5,7}

c) {3,4,7} and {7,4,3}

d) {1,2,7} and {2,7,1,4}

View Answer

Explanation: Two sets A and B are said to be equal if every element of set A is in set B and vice-versa.

{3,4,7} and {7,4,3} are equal.

2. Let A be set of prime numbers less than 6 and B be the set of prime factors of 30. Set A and B are ____________

a) Infinite

b) Empty

c) Singleton

d) Equal

View Answer

Explanation: Prime numbers less than 6 are 2,3,5. A={2,3,5}

30=2*3*5 => 2,3,5 are prime factors of 30. B={2,3,5}

Since every element of A is in B and every element of B is in A so they are equal sets.

3. A={0} and B={}. Are sets A and B are equal?

a) True

b) False

View Answer

Explanation: Set A has one element 0 while set B has no element in it and is empty so they both can’t be equal.

4. Let X be the set of letters of the word ALLOY and Y be the set of letters of the word LOYAL. Are the sets equal?

a) True

b) False

View Answer

Explanation: X={A,L,O,Y} and Y={L,O,Y,A} .

Since both sets have same elements so they are equal.

5. Which of the sets are equal?

X={x : x-4=0 and x is a natural number}, Y={ x : x^{2}=16 and x is a natural number}, Z={x : x>4 and x<16, x is a natural number}

a) X and Y

b) Y and Z

c) X and Z

d) X, Y and Z

View Answer

Explanation: x-4=0 => x=4 X={4}

x

^{2}=16 => x

^{2}-16=0 => (x-4)(x+4)=0 => x=4,-4 but -4 is not a natural number so Y={4}

x>4 and x<16 can’t be true simultaneously so Z={ }.

Hence sets X and Y are equal.

6. Which of the following sets are equal?

X={x : x is letter of word LIFE}, Y={x : x is letter of the word WIFE}, Z={x : x is letter of the word FILE}

a) X and Y

b) Y and Z

c) X and Z

d) X, Y and Z

View Answer

Explanation: X={L,I,F,E}, Y={W,I,F,E}, Z={F,I,L,E}

So, sets X and Z are equal.

7. Which of the following sets are equal?

a) {a, b, c, d} and {d, c, b, a}

b) {4,8,12,16} and {8,12,16,18}

c) {x : x is a multiple of 10} and {10,20,30}

d) {2,4,6,8} and {x : x is an even number}

View Answer

Explanation: {a, b, c, d} and {d, c, b, a} are equal sets.

{4,8,12,16} and {8,12,16,18} are not equal their elements are not matching.

{x : x is a multiple of 10} = {10,20,30,………} which is infinite set and not equal to {10,20,30}.

{x : x is an even number} = {2,4,6,………….} which is an infinite set and not equal to {2,4,6}.

8. Which of the following sets are equal?

X={1,-1}, Y={-1,1}, Z={x : x is root of x^{2}-1=0 and x is an integer}

a) X and Y

b) Y and Z

c) X and Z

d) X, Y and Z

View Answer

Explanation: X={1,-1} which is equal to Y{-1,1}.

x

^{2}-1=0 => (x-1)(x+1)=0 => x=1,-1. Z={1,-1} so set X,Y and Z are equal.

9. Equal sets _______ number of elements.

a) Must have same

b) May have same

c) Can’t have same

d) Shouldn’t have different

View Answer

Explanation: Equal sets are the sets having same number of elements with value of each element set A and B to be equal.

10. If two sets have equal number of elements, then they ___________

a) Are equal

b) Are not equal

c) May be equal

d) Are finite

View Answer

Explanation: Equal sets are the sets having same number of elements with value of each element set A and B to be equal. So, if the two sets have same number of elements, then they may or may not be equal.

11. If A = {1,10,15,17} and B = {1,5,7,8} then which of the following is the correct statement about A and B?

a) “A” and “B” are equal sets

b) “A” and “B” are equivalent sets

c) “A” and “B” are empty sets

d) “A” and “B” are infinite sets

View Answer

Explanation: Two sets are equal if each element in A is in B and vice versa. If a number of elements in both sets are the same then they are equivalent sets.

12. If A = {0}, B = {x: x is a non-negative root of x^{2}+2x=0}, C= {x: x>10 and x<5}, D = {x: x^{2}=36} then choose the correct option.

a) A=C

b) A=D

c) B=C

d) A=B

View Answer

Explanation: Here for set B the value of x = 0 since -2 is a negative root, C is a null set, also solving x

^{2}=36 gives x=6 and x =-6 Since A and B have same elements in them and also an equal number of elements, Therefore, A is equal to B.

13. If A= {1,2,3} and B= {x∈R: x^{3}-6x^{2}+11x-6=0} then A and B are equal sets?

a) True

b) False

View Answer

Explanation: The roots of x

^{3}-6x

^{2}+11x-6=0 are 1,2,3 hence A and B are the same sets so the statement is true.

14. If A={1,2} and B= {x ∈ R: x^{2}-3x+2=0} then?

a) “A” and “B” are only equivalent sets and not equal

b) “A” and “B” are equal

c) “A” and “B” are not Equivalent

d) “A” and “B” are infinite sets

View Answer

Explanation: The roots of the equation x

^{2}-3x+2=0 are 1 and 2 also A has the same elements, therefore, A and B are equal and equivalent as well as they have the same number of elements.

15. Which of the following statements are correct?

a) Equal and Equivalent sets are actually the same

b) Equivalent sets have a different number of elements

c) Equal sets have the same elements

d) Two null sets are not equal

View Answer

Explanation: If two sets A and B are equal then they are equivalent as well because all elements of A are in B and all elements of B are in A which means a number of elements in both sets are same.

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