Test the validity of the argument. Tell and show why the argument is valid or invalid.If it is warm, Brenda will go to the park or go shopping. It is warm and Brenda goes shopping. Thus, she does not go to the park.

What will be an ideal response?

Let	w = "It is warm"

p = "Brenda will go to the park"
s = "Brenda will go shopping"

If the argument is valid, the implication is a tautology. The only time that the implication could be false is if the hypothesis is true and the conclusion is false. Consider the case where p, w, and s are true, and fill in the truth values in evaluating the statement.
[(w ? (p ? s)) ? (w ? s)] ? ~p

T T

F F

(1) (3) (2)

(5)

(4)

(7) (6)

This leads to a true hypothesis (5) implicating a false conclusion (6): false (7). The implication is not a tautology and the argument is invalid.

Mathematics