Maths-
General
Easy

Question

Let X={1,2,3,4} and Y={1,3,5,7,9} . Which of the following is relations from X to Y-

  1. R subscript 1 end subscript equals left curly bracket left parenthesis x comma y right parenthesis ∣ y equals 2 plus x comma x element of X comma y element of Y right curly bracket    
  2. R subscript 2 end subscript equals left curly bracket left parenthesis 11 right parenthesis comma left parenthesis 21 right parenthesis comma left parenthesis 33 right parenthesis comma left parenthesis 43 right parenthesis comma left parenthesis 55 right parenthesis right curly bracket    
  3. R subscript 3 end subscript equals left curly bracket left parenthesis 11 right parenthesis comma left parenthesis 13 right parenthesis comma left parenthesis 35 right parenthesis comma left parenthesis 37 right parenthesis comma left parenthesis 57 right parenthesis right curly bracket    
  4. R subscript 4 end subscript equals left curly bracket left parenthesis 13 right parenthesis comma left parenthesis 25 right parenthesis comma left parenthesis 24 right parenthesis comma left parenthesis 79 right parenthesis right curly bracket    

The correct answer is: R subscript 1 end subscript equals left curly bracket left parenthesis x comma y right parenthesis ∣ y equals 2 plus x comma x element of X comma y element of Y right curly bracket


    To find the relation from X to Y.
    From the given option,
    R1 = {(x, y) : y = 2 + x, x ∈ X, y ∈ Y}
    x = 1 → y = 1 + 2 = 3
    x = 2 → y = 2 + 2 = 4
    x = 3 → y = 3 + 2 = 5
    x = 4 → y = 4 + 2 = 6
    x = 5 → y = 5 + 2 = 7
    R = {(1, 3), (2, 4), (3, 5), (4, 6), (5, 7)}
    In (4, 6), 6 ∉ either X or Y
    R1 is not a relation between X and Y.
    In R4, the element (7, 9) is present which relates set Y to set Y
    R4 is not a relation between X and Y.

    So the correct relations are R2 and R3.

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