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4.Prove that the product of two odd numbers is odd. |
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Answer» Ans :- Let a and b be two odd numbers. A number is odd if 2 will not divide evenly into it. So 2 does not divide into a or b.Look then at the product ab.2 is prime, so the only way 2 could divide into the product ab is if 2 divides into either a or b. It doesn't, so ab is odd. Look at it another way. If a and b are odd, then a and b can be written as:a=2m+1b=2n+1Where m and n are whole numbers. (Ignore negatives for the moment)Soab=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1Which is odd. PLEASE LIKE THE SOLUTION |
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