Q. 164.3( 8 Votes )

If R and S are tr

Answer :

We will prove this using an example.

Let A = {a, b, c} be a set and


R = {(a, a) (b, b) (c, c) (a, b) (b, a)} and


S = {(a, a) (b, b) (c, c) (b, c) (c, d)} are two relations on A


Clearly R and S are transitive relation on A


Now,


R S = {(a, a) (b, b) (c, c) (a, b) (b, a) (b, c) (c, b)}


Here, (a, b) R S and (b, c) R S


but (a, c) R S


R S is not transitive


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