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COMEDK202510 May 2025Morning ShiftMathematicsSets and RelationsActual

Let R be a relation on natural numbers defined by x+2 y=8, x, y N . The domain of R is

Options

  1. A1,2,3
  2. B2,4,6
  3. C2,4,8
  4. D2,4,6,8

Correct answer

B. 2,4,6

Step-by-step solution

The relation R is defined on natural numbers N = 1, 2, 3, ... by the equation x + 2y = 8 . To find the domain, we solve for x in terms of y : x = 8 - 2y . Since x must be a natural number, x 1 . Substituting the expression for x : 8 - 2y 1 2y 7 y 3.5 . Since y is a natural number, y can take values 1, 2, 3 . For y = 1 , x = 8 - 2(1) = 6 . For y = 2 , x = 8 - 2(2) = 4 . For y = 3 , x = 8 - 2(3) = 2 . The set of ordered pairs (x, y) in the relation R is (6, 1), (4, 2), (2, 3) . The domain of R is the set of all first

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