Mathematical Logic and Proving Techniques Notes

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SUBJECT: MATHEMATICAL LOGIC AND PROVING TECHNIQUES CHAPTER: PROVING TECHNIQUES METHOD 1: FORWARD-BACKWARD METHOD In mathematics, a statement is a sentence which is either true or false. Given two statement A and B: If A is true, then B is true where statement A is called as hypothesis and statement B is the conclusion. We need to convince to all that “If A is true, then B is true”, so we can use forward-backward method. Forward-Backward Method: Assume that A is true, then B is true. Step 1: Backward Process • • • • We need to show that B is true. At first, there will be no symbols from the specific problem. So, apply appropriate definitions and mathematical terminology to the specific problems. Here, you will obtain B1 or B2 or B3 and so on. Step 2: Forward Process • • • • Derive from the statement A that we assume is true. Next, apply appropriate definitions and mathematical terminology to the obtained new statement. Continue to combine and use new statement until the next statement obtained is same as the statement B1. The proof is finally complete because the assumption that A is true already reach the conclusion B2, hence B is true. There are two types of proof: 1. Analysis of proof: which is in list. 2. Condensed proof: which is in words. To understand deeply how to do proof by using the forward-backward method, look at the examples below. Website: https://mathsedu728404731.wordpress.com/ Example 1: By using the forward-backward method, prove ...
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