If 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

A. reflexive but not symmetric
B. reflexive but not transitive
C. symmetric and transitive
D. neither symmetric nor transitive

Answer

A

Explanation

Given that, A = {1, 2, 3}
and R ={(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}
` :' (1,1),(2,2),(2,3) in R`
Hence, R is reflexive.
`(1,2) in R " but " (2,1) notin R`
Hence, R is not symmetric.
`(1,2) in R " and " (2,3) in R`
`implies (1,3) in R`
Hence, R is transitive.