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let me give you a set there four elements five six seven and eight let me now give you a binary operation star on this set that is defined by this operation table in the operation table we have denoted a star B as the entry in the column headed by a and the row headed by B now what we need to find out is whether the binary operation star is commutative or not now a binary operation star on a set a is called commutative if SR B equals B star a for every a and B that belong to set a so let's take the commutativity of star and you see that five star six that is the entry in the column headed by five and the row headed by six yes we are talking about this element so five star six equals seven and what about six star five look at the table six here five here this element so we see that 6 4 5 is also 7 and this sells us that 5 star 6 equals 6 star 5 in fact if you go on checking you will find that this argument is true for all the elements of the set with us what this means is X star y equa...
