Question

If A = {1, 2, 3, 4} then which of the following is a function in A

(A) f₁ = {(x, y) : y = x + 1}

(B) f₂ = {(x, y) : x + y > 4}

(C) f₃ = {(x, y) : y < x}

(D) f₄ = {(x, y) : x + y = 5}

Answer 1

Answer is (D)

Here, f₁ = {(x, y) : y = x + 1} 

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

f₂ = {(x, y) : x + y > 4} 

= (1, 4), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4)}

f₃ = {(x, y) : y < x} 

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

f₄ = {(x, y) : x + y = 5} 

= {(x, y) : x = 5 – y} 

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

It is clear that only f₄ is a function because every element of A correspoints to unique element in B.