Mathematics Multiple Choice Questions on “Complement of a Set”.
1. What does A’ denotes when U is a universal set?
a) A
b) Φ
c) U
d) U-A
Answer: d
Clarification: Complement of a set A is a set that contains elements of U which are not the elements of A. So, A’=U-A.
2. If A= {2,3,5} and U be the set of prime factors of 210 then find A’.
a) {2,3,5}
b) {2,3,5,7}
c) {7}
d) Φ
Answer: c
Clarification: 210=2*3*5*7 => U = {2,3,5,7}.
Complement of a set A is a set which contains elements of U which are not the elements of A. So, A’=U-A={2,3,5,7} – {2,3,5} = {7}.
3. Is (A’)’=A?
a) True
b) False
Answer: a
Clarification: Complement of a set A is a set that contains elements of U which are not the elements of A. So, A’=U-A= U∩A’.
(A’)’ = (U∩A’)’ = U’∪A = A.
4. Let U = {1, 2, 3, 4, 5, 6}, A = {1,4} and B = {2,3,5}. Find A’.
a) {2,3,5,6}
b) {1,2,3}
c) {1,4,6}
d) {1,2,3,4,5,6}
Answer: a
Clarification: Complement of a set A is a set which contains elements of U which are not the elements of A. So, A’ = U – A = {1, 2, 3, 4, 5, 6} – {1,4} = {2,3,5,6}.
5. Let U = {1, 2, 3, 4, 5, 6}, A = {1,4} and B = {2,3,5}. Find B’.
a) {2,3,5,6}
b) {1,2,3}
c) {1,4,6}
d) {1,2,3,4,5,6}
Answer: c
Clarification: Complement of a set A is a set which contains elements of U which are not the elements of B. So, B’ = U – B = {1, 2, 3, 4, 5, 6} – {2,3,5} = {1,4,6}.
6. Let U = {1, 2, 3, 4, 5, 6}, A = {1,4} and B = {2,3,5}. Find A’∩B’.
a) {2,3,5,6}
b) {1,2,3}
c) {6}
d) {1,2,3,4,5,6}
Answer: c
Clarification: Complement of a set A is a set which contains elements of U which are not the elements of A. A’ = U-A = {1, 2, 3, 4, 5, 6} – {1,4} = {2,3,5,6} and B’ = U-B = {1, 2, 3, 4, 5, 6} – {2,3,5} = {1,4,6}. A’∩B’={2,3,5,6} ∩ {1,4,6} = {6}.
7. Let U = {1, 2, 3, 4, 5, 6}, A = {1,4} and B = {2,3,5}. Then A’∩B’ is equal to (A∪B)’.
a) True
b) False
Answer: a
Clarification: Complement of a set A is a set which contains elements of U which are not the elements of A. A’ = U-A = {1, 2, 3, 4, 5, 6} – {1,4} = {2,3,5,6} and B’ = U-B = {1, 2, 3, 4, 5, 6} – {2,3,5} = {1,4,6}. A’∩B’= {2,3,5,6} ∩ {1,4,6} = {6}.
A∪B = {1,2,3,4,5} => (A∪B)’={6}.
Hence, A’∩B’=(A∪B)’.
8. Which of the following is equal to A∪A’?
a) U
b) A
c) A’
d) U’
Answer: a
Clarification: In the Venn diagram, region a denotes A and region b denotes A’. Region a and b together form universal set so, A∪A’=U.
9. If A is set of equilateral triangles then A’ is ________
a) set of isosceles triangles
b) set of scalene triangles
c) union of sets of scalene and isosceles triangles
d) intersection of sets of scalene and isosceles triangles
Answer: c
Clarification: A is set of equilateral triangles i.e. triangles with all three sides equal.
Therefore, A’ is set of triangles with at least one side different i.e. may be all sides different or two sides equal so, A’ is union of sets of scalene and isosceles triangles.
10. Which of the following is not equal to set A?
a) A∩U
b) A∩Φ’
c) A∪A’
d) A∪Φ