Let A,B,C,D be sets, and consider the following:
Theorem 1. A×(B∪C)=(A×B)∪(A×C).
Theorem 2. (A×B)∩(C×D)=(A∩C)×(B∩D).
Theorem 3. (A×B)Δ(C×D)=(AΔC)×(BΔD).
For each, give a proof or counterexample.
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