We want to be able to expand our ability to use logic with mathematical statements. Many mathematical statements use variables. We say that an expression such as \(x+y=5\) is not a statement. However, if we can give more information about \(x\) and \(y\text{,}\) then we can use such an expression in a statement. For example, we could say there exists an \(x\) and \(y\) such that \(x+y=5\text{.}\) Or we could say for every \(x\) there exists a \(y\) with \(x+y=5\text{.}\) To use statements with “for every” and “there exists,” we will need to be able to understand logical statements with quantifiers.
