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Question
Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.
Options
True
False
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Solution
This statement is False.
Explanation:
Given that, R = {(3, 1), (1, 3), (3, 3)} be defined on the set A = {1, 2,
Since (1, 1) ∉ R, R is not reflexive.
Since (3, 1) ∈ R ⇒ (1, 3) ∈ R, R is symmetric.
Since, (1, 3) ∈ R, (3, 1) ∈ R
But (1, 1) ∉ R
Hence, R is not transitive.
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