Question

determine whether the compound statement

\\(p \wedge q) \
ightarrow p\\

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

first, complete the truth table:

\

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

what type of statement is \\((p \wedge q) \
ightarrow p\\)?

• tautology
• self-contradiction
• neither of these

Explanation:

Evaluate the conjunction column \(p \land q\)

$$
LATEXBLOCK0
$$

Evaluate the conditional column \((p \land q)

ightarrow p\)

$$
LATEXBLOCK1
$$

Classify the compound statement

$$
LATEXBLOCK2
$$

Answer:

Question 1

\(p\)

\(q\)

\(p \land q\)

\((p \land q)

ightarrow p\) |

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

Question 2

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