I have started a middle/highschool level geometry text. The text is warming me up for proofs by going through basic logic, which was introduced alongside Euler diagrams.
I am given the following problem:
"Each of the lettered statements below is followed by some other statements. Identify the relation of each of them to the lettered statement if possible. Write "converse," "inverse," "contrapositive," or "original statement," as appropriate.
[Below:]
"Statement D: Lady kangaroos do not need handbags."
"35) If a kangaroo is not a lady, it needs a handbag."
My question:
I believe that conditional statement D is in the form 'if not a, then b'. So: $ \neg a \Rightarrow b$.
That interpretation has a ...negation or negative at $a$ ? If that is so, I think that problem 35) is presenting the inverse which I thinking as: $\neg (\neg a \Rightarrow b)$, which resolves to be $a \Rightarrow \neg b$.
The only notation I have been exposed to so far is the conditional notation $\Rightarrow$, used so far with $a \Rightarrow b$. I have been shown "not" and assume "not" means "$\neg$". (I am sorry for any symbol confusion. I'm new to logic, stackexchange, and latex.)