Question

determine whether the compound statement is a tautology, a self-contradiction, or neither of these.

build a truth table to answer this question.

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

this is a tautology.
this is a self-contradiction.
this is neither a tautology nor a self-contradiction.

Explanation:

Construct the truth table for the sub-expressions

$$
LATEXBLOCK0
$$

Evaluate the disjunction of the sub-expressions

$$
LATEXBLOCK1
$$

Classify the compound statement

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

Answer:

• This is a tautology. (Correct answer)
• This is a self-contradiction.
• This is neither a tautology nor a self-contradiction.