symmetric and antisymmetric closed

Question

from definitoin of antisymmetry if aRb and bRa is present then a=b.

so b should be answer,though d is right,but b is more appropriate

Answer 1

no b is not correct....

(a,b) and (b,a) makes it symmetric and not antisymmetric

for relation to be symmetric and antisymetric  only self pairs are allowed

so d is ans

Comments

oh i missed the and part,if there is or given then??

Answer 2

(a) It is not symmetric since (a,c) ∈ R but (c,a) ∉ R

(b) It is symmetric but not antisymmetric.

Its by definition only.

a binary relation R on a set X is antisymmetric

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. 

So in option (b)  (aRb) with a ≠ b and (bRa) is also holding,Thats why its not antisymmetric.

Ref : https://en.wikipedia.org/wiki/Antisymmetric_relation

(c) Its also not antisymmetric.

(d) It is satisfying both the properties.