Question

complete the truth table for the compound statement: \\((\sim p \wedge \sim q) \
ightarrow (p \wedge q)\\)

\

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

Explanation:

Evaluate intermediate columns

$$
LATEXBLOCK0
$$

Evaluate conditional statement

$$
LATEXBLOCK1
$$

Answer:

\(p\)

\(q\)

\(p \land q\)

\(\sim p\)

\(\sim q\)

\(\sim p \land \sim q\)

\((\sim p \land \sim q)

ightarrow (p \land q)\) |

T	T	T	F	F	F	T
T	F	F	F	T	F	T
F	T	F	T	F	F	T
F	F	F	T	T	T	F