Question

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

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$$\begin{aligned} &p \ ightarrow q \\\\ &q \ ightarrow r \\\\ &\\therefore \\sim p \ ightarrow \\sim r \\end{aligned}$$

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

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

Explanation:

Identify the premises and conclusion of the argument

$$
LATEXBLOCK0
$$

Construct the conditional statement for argument evaluation

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

Substitute the symbolic expressions

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

Answer:

• O \([(p

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

• **O \([(p

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

• O \([(p

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