That symbol means "not"
Hypothesis (p): <u>You have a library card</u>. Conclusion (q): You can check out books.
1) If <u>you have a library card</u>, then you can check out books.
⇒Conditional
2) If you canNOT check out books, then <u>you do NOT have a library card</u>
⇒Contrapositive
3) If you can check out books, then <u>you have a library card.</u>
⇒Inverse
4) If <u>you do NOT have a library card</u>, then you canNOT check out books.
⇒Converse
5) <u>You have a library card</u> if and only if you can check out books.
⇒Biconditional
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1. p → q
2. q → p
3. ~p → ~q
4. ~q → ~p