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In this video we talk about the next concept amongst the topic of composition table or operation table we have already seen how to frame or draw a composition table in this video well be seeing a very standard numerical problem that usually comes in eye exams which is the concept of addition modulo n well also see how to draw the composition table and let's understand by reading the definition and let's see the concept in some depth lets read the definition of addition modulo n let n be a positive integer so n is a positive integer and what is the restriction given on n that it is greater than 1 means n is greater than 1 is given to me and what else is given that a and B belong to Z n where Z is a set what is the set of Z comprising it is comprising different elements which are totally n number ranging from 0 1 2 3 and so on till n minus 1 now what is this term addition modulo n what do you mean by this modulo n so modulo just is denoted by congruence modulo or multiplication modulo this word is very much common, and you'll be finding it almost everywhere in mathematics especially when you talk about binary operation so what happens is addition modulo is denoted as a plus and B that means you are basically adding two things, and then you are taking the modulo modular means you will have to find the remainder and the remainder should be very much least so the least non-negative remainder when a plus B is divided by n now again some people might be confused so lets see an example, and then we are Stan what do you mean by addition modulo n you are very much aware that Z n is a set which has how many elements n elements, and they will be ranging from zero one two till n minus one suppose I talked about the concept wherein I have the set Z and the set Z is of how many elements five elements with zero one two three four as its elements, and we are supposed to find addition modulo five that means we are supposed to find modulo five and that modulo should be addition modulo so how to find out the addition modulo what is the technique is very simple first draw the composition table as such, so you draw the composition table you write plus five here because we are talking about addition modulo so plus should come and then what you do is you just write down these elements in the first row and the first column coinciding this plus sign so zero one two three and one more four would come this can be joined and similarly zero one two three and four would come I would be presenting it this manner and now what happens is these elements when already arranged in the first row and the first column would help me to frame the whole of the table first lets join this grid and make it a complete 5×5 matrix now since this is complete lets see how to go about it, I am supposed to find addition modulo five, so the word addition just tells me that first I have to add things and side by side divided by five to obtain the result remainder lets see how to do it zero plus zero...
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