For each of the following statements about relations on a set A, where |A|=n, de

Question

For each of the following statements about relations on a
set A, where |A|=n, determine whether the statement is true
or false. If it is false, give a counterexample.
a) If R is a relation on A and |R| ? n, then R is reflexive.
b) If R1,R2 are relations on A and R2 ? R1, then 1
reflexive (symmetric, antisymmetric, transitive) ?R2 reflexive
(symmetric, antisymmetric, transitive).
c) If R1, R2 are relations on A and R2 ? R1, then R2
reflexive (symmetric, antisymmetric, transitive) ?R1 reflexive
(symmetric, antisymmetric, transitive).
d) If R is an equivalence relation on A, then n ? |R| ? n2.

Explanation / Answer

a)True b)true c)false beacuse If R1,R2 are relations on A and R2 ? R1, then 1 reflexive (symmetric, antisymmetric, transitive) ?R2 reflexive (symmetric, antisymmetric, transitive). d)true

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