Question 1178948: 1. (G • H) v (M • G)
2. G ⊃ (T • A) /A
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's analyze each of these logical arguments:
**1. (G • H) v (M • G)**
This is a statement, not an argument. It's a disjunction (OR statement) of two conjunctions (AND statements).
* **G • H:** This means "G is true AND H is true."
* **M • G:** This means "M is true AND G is true."
* **(G • H) v (M • G):** This means "Either (G and H are true) OR (M and G are true)."
To further evaluate this statement, you would need to know the truth values of G, H, and M.
**2. G ⊃ (T • A) / A**
This is an argument with a premise and a conclusion. Let's analyze its validity:
* **Premise: G ⊃ (T • A)** This means "If G is true, then (T is true AND A is true)."
* **Conclusion: A** This means "A is true."
Let's use a truth table or a logical deduction to check the validity:
**Truth Table Approach:**
| G | T | A | T • A | G ⊃ (T • A) | A |
|---|---|---|-------|-------------|---|
| T | T | T | T | T | T |
| T | T | F | F | F | F |
| T | F | T | F | F | T |
| T | F | F | F | F | F |
| F | T | T | T | T | T |
| F | T | F | F | T | F |
| F | F | T | F | T | T |
| F | F | F | F | T | F |
As you can see, there are rows where the premise "G ⊃ (T • A)" is true, but the conclusion "A" is false. Therefore, the argument is **invalid**.
**Logical Deduction Approach:**
* From the premise, we know that if G is true, then both T and A must be true.
* However, if G is false, the premise "G ⊃ (T • A)" is still true, regardless of the truth values of T and A.
* Therefore, we cannot deduce that A is necessarily true from the given premise alone.
**Conclusion:**
* The first expression is not an argument, it is a compound proposition.
* The second argument is **invalid**.
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