JEE Main202131 Aug 2021Morning ShiftMathematicsSets and RelationsActual
Which of the following is not correct for relation R on the set of real numbers?
Options
- A( x , y ) ∈ R ⇔ | x | - | y | ≤ 1 is reflexive but not symmetric.
- B( x , y ) ∈ R ⇔ | x - y | ≤ 1 is reflexive and symmetric.
- C( x , y ) ∈ R ⇔ 0 < | x - y | ≤ 1 is symmetric and transitive.
- D( x , y ) ∈ R ⇔ 0 < | x | - | y | ≤ 1 is not transitive but symmetric.
Correct answer
D. ( x , y ) ∈ R ⇔ 0 < | x | - | y | ≤ 1 is not transitive but symmetric.
Step-by-step solution
We know that ( x ,   y ) ∈ R   ,   ( y ,   x ) ∈ R   ⇒ symmetric ( x ,   y ) ∈ R   ,   ( y ,   z ) ∈ R   &   ( z ,   x ) ∈ R ⇒ transitive 0 < | x - y | ≤ 1 0 < | y - x | ≤ 1 is symmetric let 0 < | x - y | ≤ 1 .......(1) ( 1 , 2 ) ∈ R and ( 2 , 3 ) ∈ R satisfy the equation (1) but ( 1 , 3 ) ∉ R not satisfied Hence 0 < | x - y | ≤ 1 is symmetric but not tr