Question

Let p and q be two sentences in logic. Consider the following: (qvmp) => Which of the following is true?

A. It cannot be determined
B. (qv-p) => q is true when both p and q are true
C. (q v-p) => q is only true when -p is true and q is false
D. (q v-p ) => is only true when both p and q are false
E. (qv-p) => q is true when both p and q are false
F. (qv-p) => q is only true when p is false and q is false
G. (qv-p) => q is never true

Answer 1

None of the provided options correctly represent the logical statement (q ∨ -p) ⇒ q, as this conditional is a tautology and is always true when q is part of the antecedent.

Step-by-step explanation:

The question pertains to the correctness of a logical conditional disjunctive syllogism which is a common argument form in logic. The provided logical statement is incomplete: (q ∨ -p) ⇒. However, based on standard logical relationships, if we assume this to be a conditional statement where the antecedent is (q ∨ -p) and the consequent is q, it would mean that if either q is true or -p (not p) is true, then q is true. This is a tautology because if q is part of the antecedent, q will inherently be true when the antecedent is true. Therefore, the conditional (q ∨ -p) ⇒ q is always true, and none of the provided options are exactly correct. This shows the importance of understanding logical constructs such as conditionals and modus ponens.