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COMEDK2024MathematicsSets and RelationsActual

A relation R is defined from 2,3,4 to 3,6,7,10 . If x R y x and y are co prime numbers. Then range of R is

Options

  1. A3,6,7,10
  2. B2,3,4
  3. C3,7
  4. D3,7,10

Correct answer

D. 3,7,10

Step-by-step solution

The relation R is defined from the set A = 2, 3, 4 to the set B = 3, 6, 7, 10 such that x R y if and only if x and y are coprime, meaning (x, y) = 1 . We check each element of A against each element of B : For x = 2 : (2, 3) = 1 (coprime) (2, 6) = 2 (not coprime) (2, 7) = 1 (coprime) (2, 10) = 2 (not coprime) So, 2 R 3 and 2 R 7 . For x = 3 : (3, 3) = 3 (not coprime) (3, 6) = 3 (not coprime) (3, 7) = 1 (coprime) (3, 10) = 1 (coprime) So, 3 R 7 and 3 R 10 . For x = 4 : (4, 3) = 1 (coprime) (4, 6) = 2 (not coprime) (

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