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JEE Main20248 Apr 2024Evening ShiftMathematicsSets and RelationsActual

Let A= 2,3,6,8,9,11 and B= 1,4,5,10,15 . Let R be a relation on A B defined by (a, b) R(c, d) if and only if 3 a d-7 b c is an even integer. Then the relation R is

Options

  1. Aan equivalence relation.
  2. Breflexive and symmetric but not transitive.
  3. Ctransitive but not symmetric.
  4. Dreflexive but not symmetric.

Correct answer

B. reflexive and symmetric but not transitive.

Step-by-step solution

array lc A = 2,3,6,8,9,11 & ( a , b ) R ( c , d ) B = 1,4,5,10,15 & 3 ad -7 bc array Reflexive : ( a , b ) R ( a , b ) 3 ab -7 ba =-4 ab always even so it is reflexive. Symmetric : If 3 ad -7 bc = Even Case-I : odd odd Case-II : even even (c, d) R ( a , b ) 3 bc -3 ab Case-I : odd odd Case-II : even even so symmetric relation Transitive : Set (3,4) R(6,4) Satisfy relation Set (6,4) R(3,1) Satisfy relation but (3,4) R (3,1) does not satisfy relation so not transitive.

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