SOLUTION: is the argument invalid or valid? 1. R ⊃ (K • U) 2. A ⊃ (Q • R) 3. S • A ∴ U

Question 1188729: is the argument invalid or valid?
1. R ⊃ (K • U)
2. A ⊃ (Q • R)
3. S • A ∴ U
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

An argument is invalid if we have all true premises that lead to a false conclusion. Otherwise, we consider it valid.

If premise 3 was true, then both statements S and A must be true. Otherwise S * A is false. The * or dot symbol means "and" in terms of logic. Refer to "conjunction".

Since A is true, this means Q*R must be true. Recall that stuff of the form P -> Q is false when P = True and Q = false. Otherwise, P -> Q is true. The fact that statement A is true means we might have premise 2 to be false if Q*R were false. So that's why we need Q*R to be true.

If Q*R is true, then so are the individual components Q and R.

Use this line of logic to see that R being true leads to K and U being true as well (premise 1).

As you can see, all three premises are true and they lead to a true conclusion (statement U).

Therefore, this argument is valid.

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