Question

homework section 2.3: equivalent logical statements

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

is a tautology, self-contradiction, or neither of these by analyzing the statement in a truth table.

first, complete the truth table:

\

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

what type of statement is \\(q \land \sim (p \lor q)\\)?

self-contradiction
tautology
neither of these

Explanation:

Construct the truth table columns

$$
LATEXBLOCK0
$$

Determine the statement type

$$ \text{Since the final column } q \land \sim(p \lor q) \text{ contains only F values, the statement is a self-contradiction.} $$

Answer:

Question 1

First, complete the truth table:

\(p\)	\(q\)	\(p \lor q\)	\(\sim(p \lor q)\)	\(q \land \sim(p \lor q)\)
T	F	<blank>T</blank>	<blank>F</blank>	<blank>F</blank>
F	T	<blank>T</blank>	<blank>F</blank>	<blank>F</blank>
F	F	<blank>F</blank>	<blank>T</blank>	<blank>F</blank>

Question 2

What type of statement is \(q \land \sim(p \lor q)\)?

• self-contradiction (Correct answer)
• tautology
• neither of these