# Proofs: Problem 3

### Model Solution

Consider x=y=1 and z = 3.

Then $$(x \oslash y) \oslash z = (1 \oslash 1) \oslash 3 = 4 \oslash 3 = 14$$.

But $$x \oslash (y \oslash z) = 1 \oslash (1 \oslash 3) = 1 \oslash 8 = 18$$.

So $$(x \oslash y) \oslash z \not = x \oslash (y \oslash z)$$.

### Self-check

Did you give specific concrete values for x, y, and z?

Did you briefly explain why your values were a counter-example to the claim?