The symbol for if and only if is. If and only if. Once this new environment is defined it can be used normally within the document delimited it with the marks begin theorem and end theorem.
A mathematical proof is a series of logical statements.
If p and q are statements then the statement p if and only if q is defined to be true when p and q are both true or both false. The statements and reasons in a paragraph proof are written in sentences using words to explain the logical flow of the argument. See the sample proofs for examples. This is a course on PROOF WRITING with Sets This course starts with some VERY BASIC definitions regarding the theory of sets.