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Solution


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:x-y is odd positive integer or x-y=2}. The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to __________ .              [2023]

Ans.

(19)

A={0,3,4,6,7,8,9,10}

R={(x,y)∈A×A:x-y is an odd positive integer or x-y=2}

∴ Possible pairs to be added are 

{(0,3),(0,7),(0,9),(3,4),(3,6),(3,8),(3,10),(4,7),(4,9),(6,7),(6,9), (7,8),(7,10),(8,9),(9,10),(4,6),(6,8),(7,9),(8,10)}

∴  We need to add a minimum of 19 elements to form it symmetric.