This set of Compilers Multiple Choice Questions & Answers (MCQs) focuses on “Relations ”.
- (a,b) what is a?
a) Domain
b) Range
c) All of the mentioned
d) None of the mentioned
Answer
Answer: a
Explanation: A is called the domain.
- (a,b) what is b?
a) Domain
b) Range
c) All of the mentioned
d) None of the mentioned
Answer
Answer: b
Explanation: B is called the Range.
- R is said to be reflexive if aRa is true for every a in A;
a) True
b) False
Answer
Answer: a
Explanation: All the elements of A are related with
itself by relation R, hence it is a reflexive relation.
- If every aRb implies bRa then a relation R will be a symmetric relation.
a) True
b) False
Answer
Answer: a
Explanation: a is related to b by R, and if b is also related to a by the
same relation R).
- If every aRb and bRc implies aRc, then the relation is transitive
a) True
b) False
Answer
Answer: a
Explanation: a is related to b by R, and b is related to c by R, and similarly for a and c.
- The smallest set A such that A ? {1, 2} = {1, 2, 3, 5, 9} is
a) {2,3,5}
b) {1, 2, 5, 9}
c) {3, 5, 9}
d) None of the mentioned
Answer
Answer: c
Explanation: Given A ? {1, 2} = {1, 2, 3, 5, 9}. Hence A = {3,5,9}.
- If a set A has n elements, then the total number of subsets of A is.
a) N
b) 2n
c) N2
d) 2n
Answer
Answer: c
Explanation: Number of subsets of A = nC0 + nC1+ . . . . . + nCn = 2n.
8. If A n B = B, then
a) A ? B
b) A = ø
c) B ? A
d) B = ø
Answer
Answer: c
Explanation: Since A n B = B , hence B ? A .
9. Empty set is a
a) Invalid set
b) Infinite set
c) Finite set
d) None of the mentioned
Answer
Answer: c
Explanation: Empty set is a finite set.
10. If A, B and C are any three sets, then A – (B ? C) is equal to
a) (A – B) ? (A – C)
b) (A – B) ? C
c) (A – B) n (A – C)
d) (A – B) n C
Answer
Answer: c
Explanation: it is De’ Morgan law.
11. A = {x: x ? x }represents
a) {0].
b) {1}
c) {}
d) {x}
Answer
Answer: c
Explanation: That is a fact.
12. If A, B, C be three sets such that A ? B = A ? C and A n B = A n C, then
a) A=B
b) A=C
c) B=C
d) A=B=C
Answer
Answer: c
Explanation: Transition Law.
13. The number of proper subsets of the set {1, 2, and 3} is.
a) 8
b) 6
c) 7
d) 5
Answer
Answer: b
Explanation: Number of proper subsets of the set {1, 2, 3) = 2³ – 2 = 6.
14. If A and B are any two sets, then A ? (A n B) is equal to
a) A
b) B
c) A^C
d) B^C
Answer
Answer: a
Explanation: A n B ? A Hence A ? (A n B) = A.
15. If A, B and C are any three sets, then A × (B ? C) is equal to.
a) (A × B) ? (A × C)
b) (A × B) n (A × C)
c) (A ? B) × (A ? C)
d) None of the mentioned
Answer
Answer: a
Explanation: It is distributive law.
