Thread: Question on intervals

My question is:

i) Is the following statement true or false, and explain why: "If a is less than or equal to b, then (-infinity, a) is a subset of (-infinity, b)".

I drew a diagram which showed that this was true, but how would you go about proving it formally?

Any help would be appreciated

Assume then if a number then , so thus so

The standard way to prove "A is a subset of B" is to start "if , then use the definitions of A and B to conclude " ".

To prove "If a is less than or equal to b, then (-infinity, a) is a subset of (-infinity, b)":
If then p< a. Since and "<" is transitive, so .