Question

for the argument below, perform the following. a) translate the argument into symbolic form. b) determine if the argument is valid or invalid. compare the argument to a standard form or use a truth - table. if i buy more paint, then we will have enough to finish the room. we will have enough paint to finish the room. ∴ i bought more paint. a) let p be \i buy more paint\ and let q be \we will have enough paint to finish the room.\ write the argument in symbolic form. choose the correct answer below. a. p ∨ q ¬q ∴ ¬p b. p → q q ∴ p c. p ∨ q ¬p ∴ q d. p → q ¬p ∴ q b) is the given argument valid or invalid? a. the argument is valid because the argument is an example of disjunctive syllogism. b. the argument is valid because the argument is an example of the law of contraposition. c. the argument is invalid because the argument is an example of the fallacy of the inverse. d. the argument is invalid because the argument is an example of the fallacy of the converse.

Explanation:

Step1: Translate the argument

The first - statement "If I buy more paint, then we will have enough to finish the room" is a conditional statement $p
ightarrow q$. The second - statement "We will have enough paint to finish the room" is $q$, and the conclusion "I bought more paint" is $p$. So the symbolic form of the argument is $\frac{p
ightarrow q}{q}\frac{}{ \therefore p}$.

Step2: Analyze the validity

The standard form of the fallacy of the converse is: Given $p
ightarrow q$ and $q$, we cannot conclude $p$. Just because the consequent ($q$) of a conditional statement is true does not mean the antecedent ($p$) is true. For example, there could be other ways to have enough paint to finish the room without buying more paint.

Answer:

a) B. $p
ightarrow q$, $\frac{q}{ \therefore p}$
b) D. The argument is invalid because the argument is an example of the Fallacy of the Converse