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hi in this video weamp;#39;re going to discuss binary operation tables if we have a finite set s we can actually use a table to define a binary operation on the set s so letamp;#39;s say we have the finite set s of two elements and weamp;#39;ll denote those elements as a and B now we can construct this binary operation table where we have the elements a and B on this side and down here and we want to define this binary operation for a set s so remember in order to be a binary operation we actually have to have a function mapping s cross s into s so for each ordered pair in the set s cross S we need to make sure first that it gets mapped into exactly one element and second that that element is again in the set s so letamp;#39;s look at first the ordered pair a star a and we want to compute this using our binary operation so we want to see what element this gets mapped to and remember this is just the same as writing a star a so in order to be a binary operation we can either map thi