P(X) is the power set of X, where X={c, d, e, f}. A relation S is defined on P(X) as follows: for all C, D ϵ P(X), C S D <-> the number of elements in C is not equal to the number of elements in D.
Show whether T is reflexive, symmetric, or transitive.
Show whether T is an equivalence relation.

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For C from P(X), we have that C S C <=> the number of elements in C is not equal with the number of elements from C. Or this is false; hence the relation is not reflexive...

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