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Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is the brother of b . Then R is:

(A) Symmetric but not transitive

(B) Transitive but not symmetric

(C) Neither symmetric nor transitive

(D) Both symmetric and transitive.

0 2 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    3 months ago

    This is a Objective Type Question as classified in NCERT Exemplar

    Sol:

        H e r e ,     a   R   b     ⇒ a     i s     a     b r o t h e r     o f     b .       a   R   a     ⇒ a     i s     a     b r o t h e r     o f     a     w h i c h     i s     n o t     t r u e .     S o ,     R     i s     n o t     r e f l e x i v e .     a   R   b     ⇒ a     i s     a     b r o t h e r     o f     b .     b   R   a     ⇒ w h i c h     i s     n o t     t r u e     b e c a u s e     b     m a y     b e     s i s t e r     o f     a .     ⇒ a   R   b ≠ b   R   a   S o ,     R     i s     n o t     s y m m e t r i c .     N o w ,     a   R   b ,     b   R   c     ⇒ a   R   c     ⇒ a     i s     t h e     b r o t h e r     o f     b     a n d     b     i s     t h e     b r o t h e r     o f     c .     ∴ a     i s     a l s o     t h e     b r o t h e r     o f     c .

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