1. Let R be a non-empty relation on a collection of sets defined by ARB if and only if A∩B=ϕ
(a) R is reflexive and transitive
(b) R is symmetric and not transitive
(c) R is an equivalence relation
(d) R is not reflexive and not symmetric
2. The binary relation S = ф (empty set) on set A = {1, 2, 3} is
(a) neither reflexive nor symmetric
(b) symmetric and reflexive
(c) transitive and reflexive
(d) transitive and symmetric
3. Which of the following sets are null sets?
(a) {Ө}
(b) ϕ
(c) { }
(d) Both (b) & (c)
4. Number of subsets of a set of order three is
(a) 3
(b) 6
(c) 8
(d) 9
5. “n/m” means that n is a factor of m, then the relation T is
(a) reflexive and symmetric
(b) transitive and symmetric
(c) reflexive, transitive and symmetric
(d) reflexive, transitive and not symmetric
6. The number of elements in the Power set P(S) of the set S = [ [ф], 1, [2, 3] ] is
(a) 2
(b) 4
(c) 8
(d) None of these
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7. If A and B are sets and A⋃B = A⋂B, then
(a) A = ф
(b) B = ф
(c) A = B
(d) None of these
8. Let S be an infinite set and S1, S2, S3, …, Sn be sets such that S1⋃S2⋃S3⋃ . . . . . . . . . .Sn = S
then
(a) atleast one of the sets Si is a finite set
(b) not more than one of the set Si can be finite
(c) atleast one of the sets Si is an infinite set
(d) none of these
9. If X and Y are two sets, then X⋂(Y⋃X) C equals
(a) X
(b) Y
(c) ϕ
(d) None of these
10. If f:X→Y and a, b⊆X, then f(a⋂b) is equao
(a) f(a) – f
(b) (b) f(a) ⋂ f(b)
(c) a proper subset of f(a) ⋂ f(b)
(d) f(b) – f(a)
11. The number of elements in the power set of the set {{a, b}, c} is
(a) 8
(b) 4
(c) 3
(d) 7
12. If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is R
composite R?
(a) ((1, 1), (3, 1), (2, 3), (4, 2))
(b) ((1, 1), (9, 1), (4, 9), (16, 4))
(c) ((1, 1), (2, 1), (4, 3), (3, 1))
(d) ((1, 1), (2, 1), (4, 3), (3, 1))
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13. In a room containing 28 people, there are 18 people who speak English, 15 people who speak
Hindi and 22 people who speak Kannada, 9 persons speak both English and Hindi, 11 persons
both Hindi and Kannada whereas 13 persons speak both Kannada and English. How many
people speak all the three languages?
(a) 6
(b) 7
(c) 8
(d) 9
14. Order of the power set of a set of order n is
(a) n
(b) 2n
(c) n^2
(d) 2^n
16. Ina beauty contest, half the number of experts voted for Mr. A and two thirds voted for Mr.
B. 10 voted for both and 6 did not vote for either. How many experts were there in all?
(a) 18
(b) 36
(c) 24
(d) None of these
17. Let n(A) denotes the number of elements in set A. If n (A) = p and n(B) = q, then how many
ordered pairs (a, b) are there with a∈A and b∈B?
(a) p^2
(b) p×q
(c) p+q
(d) 2^pq
18. If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is
(a) symmetric only
(b) anti-symmetric only
(c) both symmetric and anti-symmetric
(d) an equivalence relation
19. The universal relation A×A on A is
(a) an equivalence relation
(b) anti-symmetric
(c) a partial ordering relation
(d) not symmetric and not anti-symmetric
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20. Let s(w) denote the set of all the letters in w where w is an English word. Let us denote set
equality, subset and union relations by =, ⊂ and ⋃ respectively.
Which of the following is NOT true?
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