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If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?

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If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y? [#permalink]

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New post 10 Aug 2017, 01:41
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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, \(x ⊙ y = 2(x^2 + y^2)\)

(2) For all y, \(0 ⊙ y = 2y^2\)
Spoiler: OA

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If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y? [#permalink]

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New post 10 Aug 2017, 01:58
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Bunuel wrote:
If ⊙ denotes a mathematical operation, does \(x⊙y = y⊙x\) for all x and y?

(1) For all x and y, \(x ⊙ y = 2(x^2 + y^2)\)

(2) For all y, \(0 ⊙ y = 2y^2\)



(1) since x and y can be interchanged
Sufficient

(2) if ⊙ denotes +
then
0 ⊙ y = 0 + 2y^2
x ⊙ y = x + 2y^2
Here x and y cannot be interchanged
but if
0 ⊙ y = 2*0^2 + 2y^2
x ⊙ y = 2*x^2 + 2y^2
Here x and y can be interchanged
Not Sufficient

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If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?   [#permalink] 10 Aug 2017, 01:58
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