Question

complete a truth table for each compound statement below.

you may want to complete the table on your own paper and insert some intermediate columns to help you arrive at the answers.

a. \sim (\sim p \lor \sim q)

\

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

b. \sim (\sim p \land q)

\

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

Explanation:

Evaluate truth values for part a

$$
LATEXBLOCK0
$$

Evaluate truth values for part b

$$
LATEXBLOCK1
$$

Answer:

Question a

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

Question b

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