The universe of discourse is the set from which the objects are taken. Math 135: how to read and do proofs. A and b are statements that are either true or false. Conditional statements are statements that are true, sometimes. Proof is a convincing argument expressed as a language of mathematics. Proof should have enough mathematical details to be convincing to the people to whom the proof is addressed. In a implies b, statement a is called the hypothesis (everything that you are assuming to be true), and statement b is the conclusion (everything you are trying to prove) To prove that a implies b is true, you must assume a is true to reach the conclusion that b is true. All other proof techniques rely on this method. In attempting to reach the conclusion b, you"ll use the backward process. By using information from hypothesis a, you"re using the forward process.