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Algebric Properties

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Algebric Properties

by Param800 » Sun Dec 30, 2012 9:25 pm
Are the following properties always true for any real number?

(1) EVEN + EVEN = EVEN
(2) EVEN - EVEN = EVEN
(3) ODD + ODD = EVEN
(4) ODD - ODD= EVEN
(5) EVEN - ODD = ODD

Please clarify. Thank You
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by Anurag@Gurome » Sun Dec 30, 2012 9:28 pm
Param800 wrote:Are the following properties always true for any real number?

(1) EVEN + EVEN = EVEN
(2) EVEN - EVEN = EVEN
(3) ODD + ODD = EVEN
(4) ODD - ODD= EVEN
(5) EVEN - ODD = ODD

Please clarify. Thank You
The odd-even concept is not valid for real numbers. To be even or odd, a real number have to be an integer first.

For integers, these properties always hold true. You can also check this with the help of examples:

(1) 2 + 4 = 6 (True)
(2) 4 - 2 = 2 (True)
(3) 1 + 3 = 4 (True)
(4) 3 - 1 = 2 (True)
(5) 4 - 1 = 3 (True)

You can try this by taking any even/odd integer, and you will find that these properties always hold true.

Hope this answers your query.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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