Whats a Mathematical Statement

Mathematical statement is a mapping from a set to a set of truth value

If you don’t specify the element from the domain, you get the open statement

We map the empty set to the truth always so any statement on the empty set result in the truth

We can define quanitifiers using and or from logic

Since it’s a function every statement from the domain can either be true or false but not both, Remember the property of functions

Another property to be a function is that you must have a corresponding element or in other words all statement have a truth value

A corollary is any statement is exactly true or false but never both

You can interpret if p then q a lot of ways. p was already a mapping