write the argument below in symbols to determine whether it is valid or invalid. State you reason for your conclusion. Specify the p and q you used. Either the koi are swimming in the pond or the birds are chirping. The birds are not chirping. The koi are swimming in the pond.
To determine the validity of the argument, we can translate it into symbolic notation using propositional variables.
Let's assign the following variables:
p: The koi are swimming in the pond.
q: The birds are chirping.
The argument can be symbolized as follows:
p ∨ q (Either the koi are swimming in the pond or the birds are chirping.)
¬q (The birds are not chirping.)
∴ p (Therefore, the koi are swimming in the pond.)
To determine the validity, we need to confirm if the premises lead to the conclusion. In this case, the premises are p ∨ q and ¬q, and the conclusion is p.
By constructing a truth table for the premises and the conclusion, we can determine if there is any assignment of truth values to p and q that would make the premises true and the conclusion false.
Here's the truth table:
p | q | p ∨ q | ¬q | p
---------------------
T | T | T | F | T
T | F | T | T | T
F | T | T | F | F
F | F | F | T | F
As we can see from the truth table, there is no row where both premises are true, and the conclusion is false. Therefore, the argument is valid.