: Composition and relation properties. For the following statements, provide a proof if the statement is true or give a counterexample if the statement is false. S and R are binary relations over the same domain. (b) If S is reflexive, then S∘S is reflexive. (c) If S and R are both anti-reflexive, then S∘R is anti-reflexive. (d) If S is anti-reflexive, then S∘S is anti-reflexive. (e) If S and R are both anti-symmetric, then S∘R is anti-symmetric. (f) If S is anti-symmetric, then S∘S is anti-symmetric.

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Q: (c) If S and R are both anti-reflexive, then S∘R is anti-reflexive.

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