Question

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

\

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

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

\

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

Explanation:

Evaluate the first truth table columns

$$
LATEXBLOCK0
$$

Evaluate the second truth table columns

$$
LATEXBLOCK1
$$

Answer:

Question 1

Complete truth table for \((p \lor q) \land (p \lor \sim q)\):

\(p\)	\(q\)	\(\sim p\)	\(\sim q\)	\((p \lor q)\)	\((p \lor \sim q)\)	\((p \lor q) \land (p \lor \sim q)\)
T	F	F	T	T	T	T
F	T	T	F	T	F	F
F	F	T	T	F	T	F

Question 2

Complete truth table for \((\sim p \land q) \lor (p \land q)\):

\(p\)	\(q\)	\(\sim p\)	\(\sim q\)	\((\sim p \land q)\)	\((p \land q)\)	\((\sim p \land q) \lor (p \land q)\)
T	F	F	T	F	F	F
F	T	T	F	T	F	T
F	F	T	T	F	F	F