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JEE Main202623 January 2026Morning ShiftMathematicsSets and RelationsActual

Let A = -2,-1,0,1,2,3,4 . Let R be a relation on A defined by x Ry if and only if 2 x+y 2 . Let l be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then l+m+n is equal to :

Options

  1. A35
  2. B34
  3. C33
  4. D32

Correct answer

C. 33

Step-by-step solution

Given A = -2, -1, 0, 1, 2, 3, 4 and xRy iff 2x + y 2 . For x = -2 : y 6 , all 7 elements valid (7 pairs). For x = -1 : y 4 , all 7 elements valid (7 pairs). For x = 0 : y 2 y -2,-1,0,1,2 (5 pairs). For x = 1 : y 0 y -2,-1,0 (3 pairs). For x = 2 : y -2 y -2 (1 pair). For x = 3, 4 : no valid y . So l = 7+7+5+3+1 = 23 . For reflexive: (x,x) R 3x 2 x 2/3 . Already present for x = -2, -1, 0 . Missing for x = 1, 2, 3, 4 , so m = 4 . For symmetric: need (y,x) R for every (x,y) R . Missing pairs: (3,-2), (4,-2), (2,-1), (3

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