Read the following statements which are taken as axioms:
$(i)$ If a transversal intersects two parallel lines,then corresponding angles are not necessarily equal.
$(ii)$ If a transversal intersects two parallel lines,then alternate interior angles are equal.
Is this system of axioms consistent? Justify your answer.

(N/A) No,this system of axioms is not consistent.
In Euclidean geometry,if a transversal intersects two parallel lines,the corresponding angles must be equal.
If we assume statement $(i)$ is true,it contradicts the fundamental property of parallel lines.
Furthermore,if corresponding angles are not equal,then the alternate interior angles cannot be equal,which contradicts statement $(ii)$.
Since the two statements lead to a logical contradiction,the system of axioms is inconsistent.