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NEST2026MathematicsSets and Relations

Let S = (x, y) x, y N , 1 x 15, 1 y 20 be a set. Let R be the equivalence relation on S defined by (x, y) R (x', y') if and only if x + y = x' + y' . Then the number of equivalence classes of R on S is

Options

  1. A34
  2. B20
  3. C15
  4. D35

Correct answer

A. 34

Step-by-step solution

Given S = (x, y) x, y N , 1 x 15, 1 y 20 . The equivalence relation R is defined as (x, y) R (x', y') if and only if x + y = x' + y' . Each equivalence class is determined by a unique value of the sum x + y . The minimum value of x + y is 1 + 1 = 2 . The maximum value of x + y is 15 + 20 = 35 . Since x and y take all integer values in their respective intervals, x + y takes all integer values from 2 to 35 . The number of distinct values of x + y is 35 - 2 + 1 = 34 . Thus, the number of equivalence classes of R on S

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