give example of a function which is symmetric and transitive but not reflexive

Asked by  | 15th Mar, 2008, 11:29: PM

Expert Answer:


Consider again the natural numbers. Define a relation, R, on the natural numbers by n R m if both n and m are even. If n R m, then both n and m are even. Hence, m R n is valid too. Thus, R is symmetric. If n R m and m R r, then n, m, and r are all even. Hence, n R r is also valid. But, 3 R 3 is not valid; hence, R is not reflexive.

Answered by  | 17th Mar, 2008, 05:46: PM

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