Answer to Question #166366 in Discrete Mathematics for faiz

Question

Translate the following argument and use a short truth table to determine whether or not the argument is valid.

Either scientists don't know what they are talking about, or the sun will eventually burn out and Earth will become dark and cold. If scientists don't know what they are talking about, then Mars is teeming with life. If Earth becomes dark and cold, then either the human race will migrate to other planets or will die out. Mars is not teeming with life, but the human race will not die out. Therefore, the human race will migrate to other planets.

S = Scientists know what they are talking about.

B = The sun will eventually burn out.

E = The Earth will become dark and cold.

M = Mars is teeming with life.

H = The human race will migrate to other planets.

D = The human race will die out.

Answer 1

We have following premises:

$\neg S\oplus(B\land E)$

$\neg S\to M$

$E\to (H\oplus D)$

$\neg M\land\neg D$

Conclusion: $H$

It cannot be row with "true" values for premises and "false" value for conclusion.

So, the given argument is valid.