Before we continue proving things, we need to learn more about how to manipulate logical expressions. We need to be able to rewrite statements as equivalent statements — create a new statement with the same truth table as the original. We have already seen an example of this in the contrapositive. In order to do that, we also need to understand how negation interacts with the disjunction, conjunction and implication. Our starting point for all of this is to think about statements which are always true.
