Answer to Question #117102 in Discrete Mathematics for Priya

Question

Is the following argument valid?

If Taxes are lowered, then income rise.
Income rise.
Therefore Taxes are lowered.

Answer 1

Let A be the expression "The taxes are lowered" and B be the expression "Income rise."

We know that "A $\Rightarrow$ B" is true. Let us now look in the truth table (https://en.wikipedia.org/wiki/Material_conditional#Definitions). We see that "A ⇒ B" is true not only when A is true. So we cannot unambiguously say that A is true (Taxes are lowered).

We may also consider another similar example.

"If the earthquake is strong, the teacup will fall from the table."

But the teacup may also fall if the cat throws it off the table. So, the phrase "Teacup fell from the table. Therefore, there is an earthquake " is not valid.