GATE 1998
March 18, 2025GATE 2000
March 18, 2025GATE 1998
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Question 38
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The binary relation R = {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4) on the set A = {1,2,3,4} is
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reflexive, symmetric and transitive
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neither reflexive, nor irreflexive but transitive
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irreflexive, symmetric and transitive
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irreflexive and antisymmetric
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Question 38 Explanation:
→ Not reflexive because (4, 4) not present.
→ Not irreflexive because (1, 1) is present.
→ Not symmetric because (2, 1) is present but not (1, 2).
→ Not antisymmetric – (2, 3) and (3, 2) are present.
It is transitive so correct option is (B).
→ Not irreflexive because (1, 1) is present.
→ Not symmetric because (2, 1) is present but not (1, 2).
→ Not antisymmetric – (2, 3) and (3, 2) are present.
It is transitive so correct option is (B).
Correct Answer: B
Question 38 Explanation:
→ Not reflexive because (4, 4) not present.
→ Not irreflexive because (1, 1) is present.
→ Not symmetric because (2, 1) is present but not (1, 2).
→ Not antisymmetric – (2, 3) and (3, 2) are present.
It is transitive so correct option is (B).
→ Not irreflexive because (1, 1) is present.
→ Not symmetric because (2, 1) is present but not (1, 2).
→ Not antisymmetric – (2, 3) and (3, 2) are present.
It is transitive so correct option is (B).