Translate the following English arguments into propositional calculus (PC) and decide, in PC, for each argument whether it is valid argument or not:

(a)

(i) If belief in God has scientific backing, then it’s rational.

(ii)

No conceivable scientific experiment could decide the issue of whether there is a God If belief in God has scientific backing, then some conceivable scientific

Therefore we conclude:

Belief in God isn’t rational.

(b) (i) Every event with finite probability eventually takes places.

(ii If the world powers don’t get rid of their nuclear weapons, then there’s a finite probability that humanity will eventually destroy the world.

(iii)

If every event with finite probability eventually takes places and there’s a finite probability that humanity will eventually destroy the world, then humanity will eventually destroy the world.

Therefore we conclude:

Either the world powers will get rid of their nuclear weapons, or humanity will eventually destroy the world.

(c) (i) If materialism is true, then idealism is false.

(ii) If idealism is true, then materialism is false.

(iii) If mental events exist, then materialism is false.

(iii) If the materialistthinksthat his or her theory is true, then mental events

exist.

Therefore we conclude:

If the materialistthinksthat his or her theory is true, then idealism is true.