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Solution


Q.

Let A = {1, 2, 3, 4} and R be a relation on the set A x A defined by R={((a,b),(c,d)):2a+3b=4c+5d}.

Then the number of elements in R is ___________ .                                                                                    [2023]

Ans.

(6)

A={1,2,3,4}

A×A={(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4), (3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

R={((a,b),(c,d)):2a+3b=4c+5d}

On checking the elements of A×A, we get:

{((1,4),(1,2)),((2,3),(2,1)),((3,1),(1,1)),((3,4),(2,2)), ((4,2),(1,2)),((4,3),(3,1))} will satisfy R.

∴Number of elements in R=6