Mathematics Multiple Choice Questions 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}
Answer: c
Clarification: 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
Answer: d
Clarification: 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
Answer: b
Clarification: 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
Answer: a
Clarification: 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
Answer: a
Clarification: 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.
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
Answer: c
Clarification: 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}
Answer: a
Clarification: {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 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
Answer: d
Clarification: 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