given the conditional statement ~p → q, which...
given the conditional statement ~p → q, which statement is logically equivalent?\no p → ~q\no ~p → ~q\no ~q → ~p\no ~q → p
Answer
# Explanation:
## Step1: Recall logical - equivalence rules
The contrapositive of a conditional statement \(a\rightarrow b\) is \(\neg b\rightarrow\neg a\), and a conditional statement is logically equivalent to its contrapositive.
For the conditional statement \(\neg p\rightarrow q\), let \(a = \neg p\) and \(b = q\).
## Step2: Find the contrapositive
The contrapositive of \(\neg p\rightarrow q\) is \(\neg q\rightarrow\neg(\neg p)\).
Since \(\neg(\neg p)=p\), the contrapositive is \(\neg q\rightarrow p\).
# Answer:
\(\neg q\rightarrow p\) (the last option)