Exercises for Section 2.4
Without changing their meanings, convert each of the following sentences into a
sentence having the form "P if and only if Q."
1. For matrix A to be invertible, it is necessary and sufficient that det(A) \neq 0.
2. If a function has a constant derivative then it is linear, and conversely.
3. If xy = 0 then x = 0 or y = 0, and conversely.
4. If a \in \mathbb{Q} then 5a \in \mathbb{Q}, and if 5a \in \mathbb{Q} then a \in \mathbb{Q}.
5. For an occurrence to become an adventure, it is necessary and sufficient for one
to recount it. (Jean-Paul Sartre)
