Assignment #3 - Due 2.1.12 - by the cancellation property...

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MAT 345 – Assignment #3 Due 2/1/12 Please write up your solutions on a separate sheet of paper. 1. Exercise 1 on page 18 of the text. 2. As we discussed in class, the algebraic properties that we use regarding equalities and inequalities all stem from the assumption of the properties listed on page 13 of the text. a. Fill in the blanks below to complete the proof of “ if ab b a - = - ) ( ” using these properties. It follows from the property of additive inverses that 0 ) ( = - + a a . Then it follows from properties of equality that b b a a ) 0 ( )] ( [ = - + Using the ______(1)_______ property, we can rewrite the equation as b b a ab = - + 0 ) ( This simplifies to ________(2)___________ using what we proved in class about the product of any real number and 0. It also follows that 0 ) ( = - + ab ab by the _______(3)__________ property. Therefore, ) ( ) ( ab ab b a ab - + = - + which can be simplified to ________(4)_______
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Unformatted text preview: by the cancellation property of addition. b. Complete the proof of the cancellation property for multiplication: If , , = c bc ac then it follows that b a = It follows from the property of additive inverses and the properties of equality that there exists a real number bc-where ) ( ) ( =-+ =-+ bc bc bc ac . Using the property proved in (a) above, we can express this equation as ) ( =-+ c b ac The distributive allows us to rewrite this equation as ) ( =-+ c b a . Since c , we know that 1/c will exist . . 3. The five properties of order can be used to prove the property for all a , 2 a or in other words, the square of any number is never negative . (Your textbook goes through a proof on page 16). Use this property to prove 1 < ....
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Assignment #3 - Due 2.1.12 - by the cancellation property...

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