Question

There does not seem to be an established symbol for the connective unless. However, Q unless P means if not P, then Q. Write the following statements in the form if P then Q. (a) I will go shopping, unless it rains. (b) The function f is continuous, unless x<2

Answer 1

See explanation below

Explanation:

There are two ways of interpreting Q unless P.

One of them is: if not P, then Q.

The other one is: if P, then not Q.

Let's write the sentences both ways

If not P, then Q

a)

Original sentence: “I will go shopping, unless it rains.”

If it does not rain, then I will go shopping.

b)

Original sentence: “The function f is continuous, unless x<2”

If x greater or equal than 2, then f is continuous.

If P, then not Q

a)

Original sentence: “I will go shopping, unless it rains.”

If it rains, then I will not go shopping

b)

Original sentence: “The function f is continuous, unless x<2”

If x<2, then f is not continuous.