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If # denotes a mathematical operation, does x#y=y#x for all

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If # denotes a mathematical operation, does x#y=y#x for all [#permalink] New post 14 Nov 2006, 17:14
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If # denotes a mathematical operation, does
x#y=y#x for all x and y?
(1) For all x and y, x#y = 2(x2 + y2).
(2) For all y, 0#y = 2 y2

I got the answer right, but I took a really long time. Can anyone please explain the science behind this?
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[#permalink] New post 14 Nov 2006, 17:23
If # denotes a mathematical operation, does
x#y=y#x for all x and y?
(1) For all x and y, x#y = 2(x2 + y2).
(2) For all y, 0#y = 2 y2


using (1)

2#3= 2( 2^2 + 3^2)

-2#3 = 2 ( (-2)^2 + 3^2)

since x and y are being squared sign doent matter

i will conclue x#y = y#x

suff

using (2)

0#y = 2 y^2

This could mean x#y = 2( x^2 + y^2)

it could also mean 2 ( x + y^2) for 0#y this would give same result as (2)

insuff
A   [#permalink] 14 Nov 2006, 17:23
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If # denotes a mathematical operation, does x#y=y#x for all

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