System of linear inequalities interpretation – UGC NET Question

Statements A, B, C and E correctly describe geometric aspects of inequalities. A states that a single linear inequality shades a half-plane. B and C distinguish between including and excluding the boundary line based on the inequality sign. E is true because shading regions on the Cartesian plane is a standard way to solve systems of inequalities. D is false because the intersection of inequalities means satisfying all of them, not just at least one. Thus A, B, C and E only are correct.

Option A:
Option A is incomplete as it excludes E and therefore misses the point that these inequalities are often solved graphically in exam problems.

Option B:
Option B is also incomplete since it omits C and thereby fails to stress the difference between strict and non-strict inequalities with respect to boundary lines.

Option C:
Option C is wrong because it omits A, which states the key half-plane interpretation.

Option D:
Option D is correct because it includes every true statement about the geometric representation and graphical solution of inequalities, while excluding D, which confuses intersection with union.