Question

determine if
\\ p \
ightarrow (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:
\

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

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

( ) tautology
( ) self-contradiction
( ) neither of these

Explanation:

Evaluate the disjunction column

$$
LATEXBLOCK0
$$

Evaluate the conditional column

$$
LATEXBLOCK1
$$

Classify the statement type

$$ \text{Since all truth values in the final column are True (T), the statement is a tautology.} $$

Answer:

Question 1

\(p\)

\(q\)

\(p \lor q\)

\(p

ightarrow (p \lor q)\) |

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

Question 2

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