Assume R and S are (nonempty) relations in a set A. Which of the following relation given below is false
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a
If R and S are transitive, then R∪S is transitive.
b
If R and S are transitive, then R ∩ S is transitive.
c
If R and S are symmetric, then R∪S is symmetric.
d
If R and S are reflexive, Then R∩S is reflexive.
answer is A.
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Detailed Solution
Consider the example: Let A={1,2,3},R={(1,1),(1,2)} and S={(2,2),(2,3)} Clearly R and S are transitive relations on A . R∪S={(1,1),(2,2),(1,2),(2,3)}R∪S is not transitive as (1,3)∉R∪S .