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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 transitive⇒R∪S is transitiveLet 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, R∪S={(1,1),(1,2),(2,2),(2,3)}Hence, (1,2),(2,3)∈R∪S⇒(1,3)∈R∪S∴R∪S is not transitive.

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