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Question
A relation R on (1, 2, 3) is given by R = {(1, 1), (2, 2), (1, 2), (3, 3), (2, 3)}. Then the relation R is ______.
Options
Reflexive
Symmetric
Transitive
Symmetric and Transitive
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Solution
A relation R on (1, 2, 3) is given by R = {(1, 1), (2, 2), (1, 2), (3, 3), (2, 3)}. Then the relation R is reflexive.
Explanation:
Let A = {1, 2, 3}
Relation on A
R = {(1, 1), (2, 2), (1, 2), (3, 3), (2, 3)}
∵ Every element of set A is related to itself
(1, 1), (2, 2), (3, 3) ∈ R
`\implies` R is reflexive.
Also (1, 2) ∈ R but (2, 1) ∉ R
So R is not symmetric
And (1, 2) ∈ R and (2, 3) ∈ R but (1, 3) ∉ R
So R is not transitive.
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