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Solution


Q.

Let A = {-4, -3, -2, 0, 1, 3, 4} and R={(a,b)∈A×A:b=|a|or b2=a+1} be a relation on A.

Then the minimum number of elements, that must be added to the relation R so that it becomes reflexive and symmetric, is ________ .                 [2023]

Ans.

(7)

R={(-4,4),(-3,3),(3,-2),(0,1),(0,0),(1,1),(4,4),(3,3)}

For reflexive, number of elements added to the relation R is  (-2,2),(-4,-4),(-3,-3)

For symmetric, number of elements added to the relation is  (4,-4),(3,-3),(-2,3),(1,0)

So, total number of elements =3+4=7