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Q.

Let  A={0,3,4,6,7,8,9,10}  and R be the relation defined on A such that  R={(x,y)A×A:xy  is odd positive integer or xy=2} . The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to ___.

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answer is 19.

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Detailed Solution

R={(3,0)(7,0)(9,0)(4,3)(6,3)(8,3)(10,3)(6,4)(7,4)(9,4)(7,6)(9,6)(8,7)(10,7)(9,8)(10,9)(8,6)(9,7)(10,8)}We need to add minimum 19 elements to form it symmetric 

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