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okay so we can actually define operations by by using a table in other words here is our table right and heres the operation in fact its the question mark now this is a binary operation now a binary operation if you think of lets say multiplication alright so lets just set up a table for multiplication real quick do a smaller scale here multiplication is one of the binary operations you use all the time its a binary operation because it operates on two elements of two things at the same exact time so if I have 3 4 here and lets say I dont know 3 4 there this could be a multiplication table which you might have your learned years ago but if you didnt heres how youd read it we take the number here 3 for example and do 3 times 3 and thats 9 you are the answer here 3 times 4 is 12 right 4 times 3 is 12 and 4 times 4 is 16 so you get this multiplication table as a binary operation because again multiplication does is it operates for example on 3 3 relates them at the sam