Question

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

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

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

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

Explanation:

Identify the 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

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

Answer:

• **(A) \([(p

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

• (B) \([(p

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

• (C) \([(p

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