Discrete Structure (DS) MCQs | Page - 19

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Q. If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1 is

(A) {(3,3), (3,4), (3,5)}
(B) {(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)}
(C) {(3,3), (3,5), (5,3), (5,5)}
(D) {(1,3), (1,5), (2,3), (2,5), (3,5), (4,5)}
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Mr. Dubey • 52.26K Points
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Q. A relation that is reflexive, anti-symmetric and transitive is a

(A) Function
(B) equivalence relation
(C) partial order
(D) None of these
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Mr. Dubey • 52.26K Points
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Q. Let f : X →Y and g : Y → Z. Let h = go f : X → Z. Suppose g is one-to-one and onto. Which of the following is FALSE?

(A) If f is one-to-one then h is one-to- one and onto.
(B) If f is not onto then h is not onto.
(C) If f is not one-to- one then h is not one-to-one.
(D) If f is one-to-one then h is one-to- one.
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Mr. Dubey • 52.26K Points
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Q. Domain and Range of the function Y = –v(–2x + 3) is

(A) x=3/2, y=0
(B) x>3/2, y=0
(C) x<3/2, y=0
(D) x=3/2, y=0
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Mr. Dubey • 52.26K Points
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Q. The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is

(A) Reflexive
(B) Transitive
(C) Symmetric
(D) Asymmetric
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Mr. Dubey • 52.26K Points
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Q. A partial ordered relation is transitive, reflexive and

(A) Anti-symmetric
(B) Bisymmetric
(C) Anti-reflexive.
(D) Asymmetric
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Q. Find the number of relations from A = {cat, dog, rat} to B = {male , female}

(A) 64
(B) 6
(C) 32
(D) 15
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Mr. Dubey • 52.26K Points
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Q. Let A = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16} and consider the divides relation on A. Let C denote the length of the maximal chain, M the number of maximal elements, and m the number of minimal elements. Which is true?

(A) C = 3, M = 8, m = 6
(B) C = 4, M = 8, m = 6
(C) C = 3, M = 6, m = 6
(D) C = 4, M = 6, m = 4
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Mr. Dubey • 52.26K Points
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Q. Consider the binary relation R = {(x,y), (x,z), (z,x), (z,y)} on the set {x,y,z}. Which one of the following is TRUE?

(A) R is symmetric but NOT antisymmetric
(B) R is NOT symmetric but antisymmetric
(C) R is both symmetric and antisymmetric
(D) R is neither symmetric nor antisymmetric
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Q. Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S are:

(A) n and n
(B) 2 n and n
(C) 2 n and 0
(D) n and 1
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