Check your answers for always, sometimes, never.

“…if and only if…” (abbreviated as “iff”) statements can be broken down into two separate “If…then…” statements. Example: I eat pizza *if and only if* I am hungry.

This would imply, 1: If I am eating pizza, then I was hungry.

and 2: If I am hungry then I will eat pizza.

Then you go about determining whether both statements are true or not.

For an “iff” statement to be true, *both* of its parts need to be completely true. I don’t actually need to use the word “completely” there. If there is one tiny example that shows when a statement is false (called a counterexample), then the entire statement is considered false, no matter how many times it seems to work as “true.”

Proofs. These proofs are admittedly lengthy and difficult. Take your time, and try your best. If you can at least follow along with the supplied explanation, I think you’ll be fine for the easier actual questions on the test.