The proposition is true since equal numbers have identical squares. However, the converse (“If x² = y², then x = y”) is false; for example, (-3)² = 3² gives 9 = 9, yet -3 ≠ 3.
Class 9 Maths Ganita Manjari Part 2 chapter 9 question answer
Class 9 Maths Ganita Manjari Part 2 chapter 9 Propositions and their Converses solutions
The proposition is true because squaring equal real quantities preserves equality. However, the converse statement—”If x² = y², then x = y”—is false. As an exact counterexample, choose x = -3 and y = 3. Their squares are equal since (-3)² = 3² = 9, but x ≠ y, because a real square has two opposite roots (x = ±y).
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