Statement: If you eat a poison, you will get sick and call your mom.
If P, then S and M
Contrapositive:
If you did not get sick or did not call your mom, you did not eat a poison.
If not S or not M, then not P.
It is important to use or here because using and would go too far.
Only If
Like the words if and then, the phrase only if can also create and if-then relationship. But it can be confusing. Even though only if ends with if it does not introduce the if-clause. In fact, only if introduce the then-clause; whatever comes immediately after only if is then then-clause. The rest of the statement is the if-clause.
Example:
Ming attends the meeting only if Hua attends.
Translation: If Ming attends the meeting, then Hua attends.
Only if you wear a shirt will you enter this restaurant.
Translation: If you enter this restaurant, then you were a shirt.
If and Only If
The phrase if and only if actually introduces two rules. Consider this example:
The Shanghai Shark will win the tournament if, and only if, it has Yao Ming as its center.
In this sentence, both if and only if introduce the last clause—“it has Yao Ming as its center.” Yet if introduces if-clause and only if introduces then-clause.
Translation: “If Shanghai Shark has Yao Ming as its center, then it will win the tournament” and “If the Shanghai Shark won the tournament, then it had Yao Ming as its center.”
