Faid L.

asked • 02/12/18

Direct proof question, "The product of an even integer and an odd integer is even".

I didnt understand 
Let say X = 2a +1 while y = 2b+1
 
Why you need to multiply xy rather x+y, as you can see below:
XY = (2a+1)(2y+1) <- correct
X+Y = 2a+1+2y+1 <- Incorrect
 
Can you elobrate why it multiply rather than add. Kinda lost. Thank you maám/sir.

1 Expert Answer

By:

Andrew M. answered • 02/12/18

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

Andrew M.

Even integers: {...,-6, -4, -2, 0, 2, 4, 6, ...}  All are multiples of 2
 
Odd integers: {..., -6+1, -4+1, -2+1, 0+1, 2+1,4+1,6+1,...}
                     {...,-5, -3, -1, 1, 3, 5, 7,...}
                     All are one more than an even integer
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02/12/18

Faid L.

Ah thank you so much sir, now I get it!
 
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02/12/18

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