Question: 3. [8 points] Truth, Lies, and Propositional Logic For each of the following propositions (also known as Boolean expressions), prove, by means of a truth

3. [8 points] Truth, Lies, and Propositional Logic For each of the following propositions (also known as Boolean expressions), prove, by means of

3. [8 points] Truth, Lies, and Propositional Logic For each of the following propositions (also known as Boolean expressions), prove, by means of a truth table, whether it is a tautology (i.e., its always true), a con- tradiction (its never true), or a contingency (its truth depends on the truth of the variables). Include the truth table as proof of each answer. (a) PVP (b) PAP (C) (PVQ)^(PV-Q)^(-PVQ)^(-PV-Q) (d) (P+Q) 4 (-Q+-P)

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