The relation​ ​ ≤ and < on a boolean algebra are defined as:

x ≤ y and only if x ∨ y = y

x < y means x ≤ y but x ≠ y

x ≥ y means y ≤ x and

x > y means y

Consider the above definitions, which of the following is not true in the boolean algebra?

(i) If x ≤ y and y ≤ z, then x ≤ z

(ii) If x ≤ y and y ≤ x, then x=y

(iii) If x < y and y < z, then x ≤ y

(iv) If x < y and y < z, then x < y