Mathematics Questions and Answers – Equal Sets

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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

Answer: c
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.
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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

Answer: d
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

Answer: b
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.
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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

Answer: a
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 : x2=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

Answer: a
Explanation: x-4=0 => x=4 X={4}
x2=16 => x2-16=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.
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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

Answer: c
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

Answer: a
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}.
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8. Which of the following sets are equal?
X={1,-1}, Y={-1,1}, Z={x : x is root of x2-1=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

Answer: d
Explanation: X={1,-1} which is equal to Y{-1,1}.
x2-1=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

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

Answer: c
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

Answer: b
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 x2+2x=0}, C= {x: x>10 and x<5}, D = {x: x2=36} then choose the correct option.
a) A=C
b) A=D
c) B=C
d) A=B
View Answer

Answer: d
Explanation: Here for set B the value of x = 0 since -2 is a negative root, C is a null set, also solving x2=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: x3-6x2+11x-6=0} then A and B are equal sets?
a) True
b) False
View Answer

Answer: a
Explanation: The roots of x3-6x2+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: x2-3x+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

Answer: b
Explanation: The roots of the equation x2-3x+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

Answer: c
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.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter