6. Determine whether the following argument is valid by completing the steps bel

Question

6. Determine whether the following argument is valid by completing the steps below. See practice problems 2 and 3 in $3.4.) If my plumbing plans do not meet the construction code, then I cannot build my house. If I hire a licensed contractor, them my plumbing plans will meet the construction code. I have hired a licensed contractor. There- fore I can build my house. a. Assign statement variables to each simple statement. (2 pts) b. State the argument form. (2 pts) c. Construct a truth table to determine the validity of the argument. (5 pts)

Explanation / Answer

Ans a)

Let P = my plumbing plans meet the construction code

Q = I hire a licensed constructor

R = I can build my house

Ans b) The argument can be represented as follows:

(a) ~P -> ~R

(b) Q -> P

(c) Q

Therefore R

By (b), (c) and Modus ponens we can conclude P.

However, (a) combined with P do not give R. Concluding R would be an inverse error.

Thus the argument is invalid with inverse error

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