For real numbers x and y, we write x R y ⇔x-y+2 is an irrational number. Then, the relation R is 

For real numbers x and y, we write x R y x-y+2 is an irrational number. Then, the relation R is 

  1. A

    reflexive

  2. B

    symmetric

  3. C

    transitive 

  4. D

    None of these

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    Solution:

    x R yx-y+2 is an irrational number.
    Let x,xR.
    Then, x-x+2=2 which is an  irrational number.
    x R x, x R
    R is reflexive .
     R is not symmetric since 2,1R since 2-1+2 is irrational  but 1,2R since1- 2+2 is not irrational  similarly R is not transtive since    -2,3R ,3,1R  but  -2,1R   .     
             

     

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