given the conditional statement ~p → q, which...
given the conditional statement ~p → q, which statement is logically equivalent?\n○ p → ~q\n○ ~p → ~q\n○ ~q → ~p\n○ ~q → p
Answer
# Explanation:
## Step1: Recall logical equivalence rules
The contra - positive of a conditional statement \(a\rightarrow b\) is \(\neg b\rightarrow\neg a\), and a conditional statement and its contra - positive are logically equivalent.
For the conditional statement \(\neg p\rightarrow q\), let \(a = \neg p\) and \(b = q\).
## Step2: Find the contra - positive
The contra - positive of \(\neg p\rightarrow q\) is \(\neg q\rightarrow\neg(\neg p)\).
Since \(\neg(\neg p)=p\), the contra - positive is \(\neg q\rightarrow p\).
# Answer:
\(\neg q\rightarrow p\)