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Question
Show that every relation which is symmetric and transitive need not to be reflexive.
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Solution
No. Let R={aRb in set I where both a and b are odd} Also R is symmetric and transitive.
∴R={(1,3),(3,1),(1,1),....}
but R is not reflexive because . (2,2),(4,4)i.e. all even integers belonging to I are not related to each other.
∴R={(1,3),(3,1),(1,1),....}
but R is not reflexive because . (2,2),(4,4)i.e. all even integers belonging to I are not related to each other.
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