TITLE: Show that the operation x is not distributive over +
QUESTION [0 upvotes]: I tried doing this question but from what I gather, it is distributive. What am I doing wrong? This is what I've done so far for the question:

P.S: the binary operations are not regular multiplication and addition, I specify them in the photo.

REPLY [1 votes]: Hint: I don't know whether you noticed, but consider how similar your operations are to addition and multiplication on fractions (what is $\frac ab+\frac cd$?) It just looks like you aren't allowed to simplify. Should make the rules much easier to remember and work with.
Also, if you're supposed to disprove distributivity, you don't have to use $a,b,c,d,e,f$. It's enough to find just one set of specific numbers where it doesn't work. That will probably also help you focus your attention where it should be, namely on the overarching logic, not on the rote calculations.

REPLY [0 votes]: Have you tried the other order? Pay particular attention to the second coordinate.
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