What is the truth value of the sentence "P v ~ P"?
To determine the truth value of the sentence "P v ~P", we need to analyze its logical structure. The sentence "P v ~P" is a logical expression that consists of two parts: the proposition "P" and its negation "~P", connected by the logical operator "v" (which stands for "or").
In order to evaluate the truth value of "P v ~P", we need to consider two possible cases.
1. If proposition P is true, then ~P (not P) is false. In this case, when we evaluate "P v ~P", we find that P v ~P is true because at least one of the two propositions is true.
2. If proposition P is false, then ~P (not P) is true. In this case, when we evaluate "P v ~P", we find that P v ~P is again true because at least one of the two propositions is true.
Based on these two possible cases, we can conclude that "P v ~P" is always true, regardless of the truth value of proposition P.