deductive reasoning

Deductive Reasoning : reasoning in which the conclusion is based on statements that areaccepted as true.http://www.edcollins.com/logic/index.htmlTwo Column Proofs: these are tools a mathematician uses to communicate his thoughtsto other people. A two column proof is used to clearly explain how a mathematical orlogical result is obtained.1. Solve the equation 3(x + 4) - 5 = x + 13. Use a two column proof to explain yourwork.StatementsReasonsTitle: Apr 21­8:39 AM (1 of 9)

Even IntegersOdd IntegersTitle: Apr 21­9:50 AM (2 of 9)

Prove that the sum of two odd integers is an even integer.StatementsReasonsTitle: Apr 21­9:52 AM (3 of 9)

Prove that the square of an odd number is always odd.StatementsReasonsTitle: Apr 21­9:53 AM (4 of 9)

Conditions for Congruent TrianglesTitle: Apr 21­9:55 AM (5 of 9)

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Refexive Property : this word is used as the reason when we want to say that anumber is equal to itself.Title: Apr 21­10:04 AM (8 of 9)

Homework: Set up two column proofs for each of these statements.1. page 410: 3,6,92. The solution to 2(5x + 1) + 7 = 3(x - 2) + 43 is x = 4.3. The solutions to are x = 4 and x = -24. The product of an even number with an odd number is even.5. The square of an even number plus and odd number is always odd.Title: Apr 21­10:10 AM (9 of 9)