What is expected of you if you are asked to prove something? What distinguishes a correct proof from an incorrect one? This book is intended to help students learn the answers to these …

A proof must always begin with an initial statement of what it is you intend to prove. It should not be phrased as a textbook question (“Prove that....”); rather, the initial statement should be …

For all integers n, if n is even, n2 is even. For any sets A and B, if A ⊆ B and B ⊆ A, then A = B. For all sets S, |S| < | ℘ (S)|. Everybody's looking forward to the weekend, weekend. How do …

Proof by Induction Suppose we wish to prove a certain assertion concerning positive integers. Let A(n) be the assertion concerning the integer n. To prove it for all natural numbers n>=1, we …

There are four basic proof techniques to prove p =) q, where p is the hypothesis (or set of hypotheses) and q is the result. What follows are some simple examples of proofs. You very …

Practice. ite -co umn proof for the following problems. 11. 12. Given: C Prove:

Throughout this course, you will be asked to “prove” or “show” certain facts. As such, you should know the basics of mathematical proof, which are explained in this document.