Question

Let p and q be two sentences in logic consider the following (q v ~p) => q 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

The statement '(q v ~p) => q' is always true when q is true, regardless of p's value. It is a conditional logical expression where q's truth guarantees the implication's truth.

Step-by-step explanation:

Let us analyze the logical expression (q v ~p) => q to determine its truth value. This expression is a conditional statement, where 'q v ~p' is the antecedent (if part), and 'q' is the consequent (then part). The logical operator 'v' stands for 'or', and '~' stands for 'not'. The arrow '=>' represents logical implication.

If the antecedent is true or the consequent is true, the implication is true. Therefore, if q is true, regardless of p's value, the implication will always be true, because the truth of q makes the consequent true. If q is false and p is true, the antecedent 'q v ~p' is false since neither q is true nor is ~p (not p) true, so the implication would again be true because a false antecedent leads to a true implication. Thus, the correct answer is B: '(q v ~p) => q is true when both p and q are true', and it is also true in other cases as described.