(6)

Given,

Set A= {1,2,3,4}

And relation on A x A as 2a + 36 = 4c + 5d

Now, Maximum value of 2a + 3b = 20 at (4, 4)

And Minimum value of 4c + 5d = 9 at (1, 1)

So, 4c + 5d can be equal to 9, 13, 14, 17, 18, 19

Now 2a + 36 can be 9 if (a, b) = (3, l) (c, d) = (l, 1)

Similarly, 2a +3b can be 13, if (a, b) = (2, 3) (c, d) = (2, 1)

And 2a + 3b can be 14, if (a, b) = (4, 2) or (1, 4)

(c, d) = (1, 2)

Similarly, 2a +3b can be 17, if (a, b) = (4, 3) (c, d) = (3, 1)

And 2a + 3b can be 18 if (a, b) = (3, 4)

(c, d) = (2,2)

Hence, there are total 6 elements which satisfy the given relation.

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