Question

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complete the truth table:

\

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

Explanation:

Evaluate basic operations and negations

$$
LATEXBLOCK0
$$

Evaluate conjunction of negations

$$
LATEXBLOCK1
$$

Evaluate conditional statement

$$
LATEXBLOCK2
$$

Answer:

\(p\)

\(q\)

\(p \land q\)

\(\sim p\)

\(\sim q\)

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

\((p \land q)

ightarrow (\sim p \land \sim q)\) |

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