In this problem U will denote the universal set: the set of all fruit. A will denote the set of apples, B will denote the set of bananas, and P(x, y) will denote the open sentence “x tastes better than y".

Write the following statements using quantifier notation and logical operations. Don’t worry about which of these are true or false.

Apples always taste better than bananas.

Apples and bananas are the only kind of fruit.

Only bananas taste better than apples.

Some fruits are bananas.

To taste better than all apples, a fruit needs to be a banana