[dxbydt]

Here's a terribly amusing one on Z3. https://imgur.com/a/RZwHkLV

First it says I don't know the answer to 1+2. Then it says ofcourse 1+2 must be 1. In either case, its the same exact question, and if you assert closure on 3 elements, with 1+1=3 and 1+3=2, you are left with no choice other than 1+2=1 because closure and Cayley Hamilton. The very first property it lists is closure! So it knows what closure is, but doesn't know how to use it. But give it the answer to 2+1 and suddenly it uses associativity !