Question

homework section 2.3: equivalent logical statements

question 3

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 components

$$
LATEXBLOCK0
$$

Evaluate the final column

$$ \forall (p, q), \quad (q ightarrow p) \vee (\sim q ightarrow p) \equiv \text{T} $$

Answer:

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