34. The relation “divides” on a set of positive integers is ________.

(A) Symmetric and transitive

(B) Anti symmetric and transitive

(C) Symmetric only

(D) Transitive only

Answer B.

Consider the Equality (=) relation on R: Equality is reflexive since for each x ∈ R, x = x.

 Equality is symmetric since for each x,y ∈ R, if x = y, then y = x. Equality is transitive since for each x,y,z ∈ R, if x = y and y = z, then x = z.

Let we have set {2,4,6,8}

If  4 is divisible by 2. Then 2is not divisible by 4. So we can say it is not symmetric.

If x/y and y/z then x/z. it is transitive.

Antisymmetric relation. if R(a,b) and R(b,a), then a = b, or, equivalently, if R(a,b) with a ≠ b, then R(b,a) must not hold.

R(2,2 ) holds.

R(4,4) holds

-          So on

R(4,2 ) exists but R(2,4) doesnot exist.

R(8,2)exists but R(2,8) dosenot exist. Hence it is anti symmetric.