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Originally Posted by

**kurac** Hi, Im determining which relations are reflexsive, transitive, summetric or antisymmetric on set A = {x,y,z}.

Ive come up with following:

1) {(x,y), (y,x)} = symmetric

correct!

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2) {(x,x), (y,y)} = reflexsive

incorrect! the correct answer is "neither". note that $\displaystyle (z,z)$ is not in the set. so it's not reflexive.

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3) {(x,x) , (y,y), (z,z), (x,z)} = reflexsive

incorrect! reflexive and transitive.

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4) A^2 = reflexsive, symmetric, transitive

correct!

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5) 0 (empty set) = neither (im not sure on this one)

incorrect! symmetric and transitive but not reflexive.

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6) {(x,y), (x,x), (x,z)} = reflexsive

incorrect! transitive.