Question

question
select the statement that is the inverse of the following statement:
if alexandra eats peanuts, then she will break out in hives.

answer
if alexandra doesnt eat peanuts, then she wont break out in hives.
if alexandra breaks out in hives, then she has eaten peanuts.
if alexandra doesnt break out in hives, then she hasnt eaten peanuts.
if alexandra eats peanuts, then she wont break out in hives.

Explanation:

To find the inverse of a conditional statement "If \( p \), then \( q \)", we negate both the hypothesis (\( p \)) and the conclusion (\( q \)). The original statement is "If Alexandra eats peanuts (\( p \)), then she will break out in hives (\( q \))". Negating \( p \) gives "Alexandra doesn't eat peanuts" and negating \( q \) gives "she won't break out in hives". So the inverse is "If Alexandra doesn't eat peanuts, then she won't break out in hives".

Answer:

If Alexandra doesn't eat peanuts, then she won't break out in hives.