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Let $S=\{a,b\}$

Here are the two binary operations (I'm not sure how to format the tables here):

$*|a$ $b$ -------- $*|a$ $b$

$a|a$ $a$ -------- $a| a$ $b$

$b|a$ $b$ --------- $b| b$ $b$

Usually when I show something is associative, I have three elements, so I'm not sure how to go about showing associativity here.

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