MathDB

Operation problem

Source:

December 25, 2005

Problem Statement

If the operation

x * y

is defined by

x * y = (x+1)(y+1) - 1

, then which one of the following is FALSE?

<span class='latex-bold'>(A)</span> \ x * y = y *x

for all real

x

and

y

.

<span class='latex-bold'>(B)</span> \ x * (y + z) = ( x * y ) + (x * z)

for all real

x,y,

and

z

<span class='latex-bold'>(C)</span> \ (x-1) * (x+1) = (x * x) - 1

for all real

x

.

<span class='latex-bold'>(D)</span> \ x * 0 = x

for all real

x

.

<span class='latex-bold'>(E)</span> \ x * (y * z) = (x * y) * z

for all real

x,y,

and

z

.

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