A relation R on a set A is said to be GO iff ∀a,b [ (aRb ∧ bRa) ↔ (a = b) ], where a,b∈A.
- a, b are related to each other iff a = b; AND
- a not related to b OR b not related to a iff a ≠ b.
Option A : From point 1, we can say that aRa, where a∈A. Thus, reflexive.
Option B : From point 2, we can say that at most one of aRb and bRa is possible, where a,b∈A and a≠b. Thus, not symmetric.
Option C : From point 1, we can say that aRb and bRa iff a=b, where a,b∈A . Thus, anti-symmetric.
Option D : Let aRb and bRc, then also it is possible that a is not related to c, where a,b,c∈A and a≠b≠c. (See point 2). Thus, not transitive.
Answer :- A, C