Question

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

\

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

Explanation:

Evaluate negations of q and r

$$
LATEXBLOCK0
$$

Evaluate conditional statement

$$
LATEXBLOCK1
$$

Evaluate final disjunction

$$
LATEXBLOCK2
$$

Answer:

\(p\)

\(q\)

\(r\)

\(\sim q\)

\(\sim q

ightarrow p\) | \(\sim r\) | \((\sim q
ightarrow p) \lor \sim r\) |

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