(Solved): 1. How many rows appear in a truth table for each of these compound propositi ...

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1. How many rows appear in a truth table for each of these compound propositions? a) \( (q \rightarrow \neg p) \vee(\neg p \rightarrow \neg q) \) b) \( (p \mathrm{v} \neg t) \wedge(\mathrm{p} \vee \neg \mathrm{S}) \) c) \( (p \rightarrow r) \vee(\neg \mathrm{S} \rightarrow \neg t) \vee(\neg u \rightarrow v) \) d) \( (p \wedge r \wedge \mathrm{s}) \vee(q \wedge t) \vee(r \wedge \neg t) \) 2. Construct a truth table for each of these compound propositions. a) \( p \rightarrow \neg p \) b) \( p \leftrightarrow \neg p \) c) \( p \oplus(\mathrm{p} \vee q) \) d) \( (p \wedge q) \rightarrow(p \vee q) \) e) \( (q \rightarrow \neg p) \leftrightarrow(p \leftrightarrow q) \) f) \( (p \leftrightarrow q) \oplus(p \leftrightarrow \neg q) \) 3. Construct a truth table for each of these compound propositions. a) \( p \oplus p \) b) \( p \oplus \neg p \) c) \( p \oplus \neg q \) d) \( \neg p \oplus \neg q \) e) \( (\mathrm{p} \oplus \mathrm{q}) \vee(\mathrm{p} \oplus \neg \mathrm{q}) \) f) \( (p \oplus q) \wedge(p \oplus \neg q) \)