Question

Write a statement that is equivalent to ~ p->q?

Answer 1

If you take any logic statement, flip it, and then negate it, it too will be true.

"If it's Saturday, then I won't be in School"
1. flip it: "I am not in School, therefore it must be Saturday"
This is called the converse, which is not always true (as in this case, it could easily be Sunday, or the summer), but it can be sometimes.
2. now negate it: "I am in school, therefore it must not be Saturday"
If the original statement is true, than this (the inverse of the converse, aka the contrapositive) will always be true.

\(\sim p \rightarrow~~~ q\) This is given, so you assume it's true
flip it: \(q \rightarrow \sim p\) Not necessarily true, on fact, usually false, but not always
negate it: \(\sim q \rightarrow ~~\, p\) Always true if the given is true

Now the contrapositive is not equivalent or identical by any means to the original statement, but it is another true statement.

I could have read the question incorrectly; it could be asking for a real-world scenario. In that case, you could say something like "If I don't have the latest book in the series, then I will buy it."