If ⊙ denotes a mathematical operation, does

[BTGmoderatorDC]

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, \(0 ⊙ y = 2y^2\)





OA A

Source: Official Guide

[swerve]

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, \(0 ⊙ y = 2y^2\)





OA A

Source: Official Guide

Statement 1, since x and y can be interchanged, then sufficient. \(\Large{\color{green}\checkmark}\)

Statement 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, then not sufficient. \(\Large{\color{red}\chi}\)

Therefore, __A__