Let R,S be binary relations on a non-empty set A. Consider thefollowing:
Theorem 1. If R,S are both reflexive, then R∖S is reflexive.
Theorem 2. If R,S are both symmetric, then R∩S is symmetric.
Theorem 3. If R,S are both transitive, then RΔS istransitive.
For each, give a proof or a counterexample.
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