Consider the following statements:
(I). If \(R_1\)and \(R_2\) are equivalence relations on \(X\) then \(R_1\cap R_2\) is also an equivalence relation.
(II). If \(R_1\)and \(R_2\) are equivalence relations on \(X\) then \(R_1\cap R^{-1}_2\) is also an equivalence relation.
(III). If \(R\) is irreflexive and transitive then R is antisymmetric.
Which of the above statements is/are TRUE?
1
I and II only
2
II only
3
I and III only
4
All are true
5
Question Not Attempted