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Let R be the relation on the set A={1,\ ...

Let `R` be the relation on the set `A={1,\ 2,\ 3,\ 4}` given by `R={(1,\ 2),\ (2,\ 2),\ (1,\ 1),\ (4,\ 4),\ (1,\ 3),\ (3,\ 3),\ (3,\ 2)}` . Then,
(a) `R` is reflexive and symmetric but not transitive
(b) `R` is reflexive and transitive but not symmetric
(c) `R` is symmetric and transitive but not reflexive
(d) `R` is an equivalence relation

Text Solution

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`R={(1,\ 2),\ (2,\ 2),\ (1,\ 1),\ (4,\ 4),\ (1,\ 3),\ (3,\ 3),\ (3,\ 2)}`
`(A,\ A) in R` for every `A={1,\ 2,\ 3,\ 4}`
R is reflexive.
`(1,\ 2) in R` but `(2,\ 1) notin R`
R is not symmetric.
`(a,\ b), (b,\ c) in R AA a, b, c in {1,\ 2,\ 3,\ 4}`
R is not transitive.

R is reflexive and transitive but not symmetric
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