91Ó°ÊÓ

Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible. Every real number is an even integer.

For matrix \(A\) to be invertible, it is necessary and sufficient that \(\operatorname{det}(A) \neq 0\).

Use truth tables to show that the following statements are logically equivalent. P \wedge(Q \vee R)=(P \wedge Q) \vee(P \wedge R)

Translate each of the following sentences into symbolic logic. If \(f\) is a polynomial and its degree is greater than 2 , then \(f^{\prime}\) is not constant.

If a function has a constant derivative then it is linear, and conversely.

Negate the following sentences. If \(x\) is prime, then \(\sqrt{x}\) is not a rational number.

Translate each of the following sentences into symbolic logic. If \(x\) is prime, then \(\sqrt{x}\) is not a rational number.

Translate each of the following sentences into symbolic logic. For every prime number \(p\) there is another prime number \(q\) with \(q>p\).

Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible. Some sets are finite.

Translate each of the following sentences into symbolic logic. I don't eat anything that has a face.