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Let R be the relation in the set {1,"...

Let R be the relation in the set `{1," "2," "3," "4}` given by `R" "=" "{(1," "2)," "(2," "2)," "(1," "1)," "(4," "4)," "(1," "3)," "(3," "3)," "(3," "2)}` . Choose the correct answer. (A) R is reflexive and symmetric but not transitive. (B) R is re

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

Verified by Experts

The correct Answer is:
B
`because (1, 1), (2, 2), (3, 3), (4, 4) in R`
`therefore R` is reflexive.
`because (1, 2) in R but (2, 1) notin R`
` therefore R` is not symmetric.
If `(a, b) in R, (b,c) in R `then `(a, c) in R`
`rArr R ` is transitive.
Therefore, R is reflexive and transitive but not symmetric.
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