Question

complete the truth table for the compound statement: \\((p \lor q) \land (\sim p \lor \sim q)\\)

\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline p & q & \\sim p & \\sim q & (p \\lor q) & (\\sim p \\lor \\sim q) & (p \\lor q) \\land (\\sim p \\lor \\sim q) \\\\ \\hline t & t & ? & ? & ? & ? & ? \\\\ \\hline t & f & ? & ? & ? & ? & ? \\\\ \\hline f & t & ? & ? & ? & ? & ? \\\\ \\hline f & f & ? & ? & ? & ? & ? \\\\ \\hline \\end{array}$$

Explanation:

Evaluate the first truth table columns

$$
LATEXBLOCK0
$$

Evaluate the second truth table columns

$$
LATEXBLOCK1
$$

Answer:

Question 1

\(p\)	\(q\)	\(\sim p\)	\(\sim q\)	\((\sim p \wedge q)\)	\((p \vee q)\)	\((\sim p \wedge q) \vee (p \vee q)\)
T	F	F	T	F	T	T
F	T	T	F	T	T	T
F	F	T	T	F	F	F

Question 2

\(p\)	\(q\)	\(\sim p\)	\(\sim q\)	\((p \vee q)\)	\((\sim p \vee \sim q)\)	\((p \vee q) \wedge (\sim p \vee \sim q)\)
T	F	F	T	T	T	T
F	T	T	F	T	T	T
F	F	T	T	F	T	F