Question

Determine whether the argument is valid or invalid The actors will play in a movie if and only if the sky is blue. Garen is a captain or the sky is blue. Garen is not a captain. Therefore, the actors will not play in a movie

Answer 1

The argument given is invalid because it concludes that the actors will not play in a movie despite the premises suggesting that if the sky is blue, the actors will play in a movie, and nothing about the sky being not blue was established.

Step-by-step explanation:

To determine whether the argument is valid or invalid, we need to analyze the logical structure. The provided argument can be broken down into propositions and examined using logical connectives:

1. The actors will play in a movie if and only if the sky is blue.
2. Garen is a captain or the sky is blue.
3. Garen is not a captain.
4. Therefore, the actors will not play in a movie.

Looking at propositions 2 and 3 together:
If Garen is not a captain (proposition 3), it follows from proposition 2 that the sky must be blue. From the first proposition, if the sky is blue, then the actors will play in a movie. Therefore, the conclusion that 'the actors will not play in a movie' does not follow from the premises and the argument is invalid.