Question

use a truth table to determine whether or not the argument given in symbolic form is valid or invalid.

premise 1: \\(p \
ightarrow \sim q\\)
premise 2: \\(q\\)
conclusion: \\(\therefore \sim p\\)

a. choose the compound statement you must evaluate to determine whether the argument is valid or invalid.

\\(\bigcirc (p \
ightarrow \sim q) \wedge q \
ightarrow \sim p\\)
\\(\bigcirc (p \
ightarrow \sim q) \vee q \
ightarrow \sim p\\)
\\(\bigcirc (p \
ightarrow \sim q) \wedge q \wedge \sim p\\)

Explanation:

Identify premises and conclusion

$$
LATEXBLOCK0
$$

Formulate the conditional statement for argument validity

$$ [(\text{Premise 1}) \wedge (\text{Premise 2})] ightarrow \text{Conclusion} $$

Substitute the symbolic expressions

$$ [(p ightarrow \sim q) \wedge q] ightarrow \sim p $$

Answer:

• **(A) \([(p

ightarrow \sim q) \wedge q]
ightarrow \sim p\) (Correct answer)**

• (B) \([(p

ightarrow \sim q) \vee q]
ightarrow \sim p\)

• (C) \([(p

ightarrow \sim q) \wedge q] \wedge \sim p\)