Question
Let A be the non – empty set of children in a family. The relation ‘x is a brother of y’ in A is
Answer: Option C
:
C
Let R denotes the relation ‘is brother of ‘. Let X ϵ A. If x is a girl, then we cannot say that x is brother of x.
∴ (x,x) /ϵ R ∴ R is not reflexive.
Let (x, y) ϵ R ∴ x is a brother of y.
∴ y may or may not be a boy.
∴ we cannot say that (y, x) ϵ R.
∴ R is not symmetric.
Let (x, y) ϵ and (y, z) ϵ R.
∴ x is a brother of y and y is a brother of z
⇒ is brother of z ⇒ (x, z) ϵ R
∴ R is transitive.
∴ The correct answer is (c).
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:
C
Let R denotes the relation ‘is brother of ‘. Let X ϵ A. If x is a girl, then we cannot say that x is brother of x.
∴ (x,x) /ϵ R ∴ R is not reflexive.
Let (x, y) ϵ R ∴ x is a brother of y.
∴ y may or may not be a boy.
∴ we cannot say that (y, x) ϵ R.
∴ R is not symmetric.
Let (x, y) ϵ and (y, z) ϵ R.
∴ x is a brother of y and y is a brother of z
⇒ is brother of z ⇒ (x, z) ϵ R
∴ R is transitive.
∴ The correct answer is (c).
Was this answer helpful ?
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