Final answer:
To determine the validity of the argument, we can simplify the premises and construct a truth table to check if the conclusion is true in all rows where the premises are true. After doing so, we find that the conclusion is true in all valid rows, indicating that the argument is valid.
Step-by-step explanation:
In this question, we are given the premises (∼G ∨ E) • (R ∨ M) and R ∨ ∼G, and we are asked to determine the validity of the argument. To do this, we can simplify the premises using logical rules.
Using the distributive property, we can simplify (∼G ∨ E) • (R ∨ M) to (∼G • R) ∨ (∼G • M) ∨ (E • R) ∨ (E • M).
Next, using the distributive property again, we can simplify (∼G • R) ∨ (∼G • M) ∨ (E • R) ∨ (E • M) to (E • R) ∨ (∼G • M). Now we have the simplified premises (E • R) ∨ (∼G • M) and R ∨ ∼G.
To determine the validity of the argument, we can construct a truth table for the premises (E • R) ∨ (∼G • M) and R ∨ ∼G, along with the conclusion E ∨ M. If the conclusion is true in all rows where the premises are true, then the argument is valid. After constructing the truth table, we find that the conclusion E ∨ M is true in all rows where the premises are true. Therefore, the argument is valid.