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Question

Let R and S be two non-void relation on a set A. Which of the following statement is false

A
R and S are transitiveRS is transitive
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B
R and S are transitiveRS is transitive
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C
R and S are symmetricRS is symmetric
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D
R and S are reflexiveRS is reflexive.
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Solution

The correct option is A R and S are transitiveRS is transitive
Let A={1,2,3}

Let the two transitive relations on set A be

R={(1,1),(1,2)}

and S={(2,2),(2,3)}

Now, RS={(1,1),(1,2),(2,2),(2,3)}

Hence, (1,2),(2,3)RS

(1,3)RS

RS is not transitive.

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