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Question
Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. Then R is ______.
Options
Reflexive but not symmetric
Reflexive but not transitive
Symmetric and transitive
Neither symmetric, nor transitive
Solution
Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. Then R is reflexive but not symmetric.
Explanation:
Given that, A = {1, 2, 3}
R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3),(1, 3)}
∵ (1, 1), (2, 2),(3, 3) ∈ R
Hence, R is reflexive.
(1, 2) ∈ R but (2, 1) ∉ R
Hence, R is not symmetric.
(1, 2) ∈ R and (2, 3) ∈ R
⇒ (1, 3) ∈ R
Hence, R is transtive.
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