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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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