Question

How are contrary propositions P and Q represented in terms of logical operations?

a) P and Q are both true
b) P and Q are both false
c) P and Q are logically equivalent
d) P and not(Q) are logically equivalent

Answer 1

Contrary propositions are represented as one being true if and only if the other is not true, such as P and not(Q) being logically equivalent.

Step-by-step explanation:

How are contrary propositions P and Q represented in terms of logical operations? The answer to this question is d) P and not(Q) are logically equivalent. This means P is true if and only if Q is not true. Contrary propositions cannot both be true at the same time, but they can both be false. To illustrate, if P is 'It is raining,' then not(Q) could be 'It is not sunny,' assuming 'It is sunny' is Q. While it can't both rain and be sunny at the same time (contrary), it can be cloudy (both false).