Given the conditional statement ~p → q, a logo equivalent include the following: D. ~q → p.
In Mathematics, a conditional statement is a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement has the form "if p then q."
p → q
Where:
p and q represent sentences or statements.
Generally speaking, two expressions are considered as being logically equivalent if they have the same truth value for all possible combinations of truth values and for all variables that appear in both expressions.
This conditional statement ~p → q means if not p, then q;
where:
- p is the antecedent
- q is the consequent.
In this context, we can logically deduce that the negation of the consequent, q, would be sufficient to state the negation of the antecedent, not p (double negation of p). Symbolically, this can be represented as follows:
~q → ~(~p) ≡ ~q → p