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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