by Let A = {1, 2, 3, 4, 5). Define ...
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by Let A = {1, 2, 3, 4, 5). Define an operation av b = max (a, b). Prepare its composition table. Show that A is closed for the given operation is commutative. Closed for the given operation and that the given operation

11th - 12th Class
Maths
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SOLUTION We prepare the table as given below. begin{tabular}{c|ccccc} ( vee ) & 1 & 2 & 3 & 4 & 5 hline 1 & 1 & 2 & 3 & 4 & 5 2 & 2 & 2 & 3 & 4 & 5 3 & 3 & 3 & 3 & 4 & 5 4 & 4 & 4 & 4 & 4 & 5 5 & 5 & 5 & 5 & 5 & 5 end{tabular} Closure Property since all the entries of the composition table are from the given set, so closure property is satisfied. Commutative Law Clearly, every row coincides with the corresponding column. So, commutative law is satisfied.
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