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Prove (p∧? q)∨(? p∧q)? (p∨q)∧? (p∧q)?
Two methods

1. chart method, you list the truth values of all expressions, which is troublesome but intuitive.

2. Identity method

(p∧? q)∨(? p∧q)

=[(p∧? q)∨? p]∧[(p∧? Q)∞q]- distribution law

=[(p∨? p)∧(? q∨? p)]∧[(p∨q)∧(? Q∨q)]-distribution law

=[T∧(? q∨? P)]∧[(p∨q)∧T]-Negative Law

=(? q∨? P)∧(p∨q)-identity law

=(p∞q)∧(? q∨? P)-commutative law

=(p∞q)∧? (p∧q)-De Morgan's Law