Paper 1 · Logical Reasoning
UGC NET June 2024 Re-Exam (28.08.2024) Shift-I
Which of the following two propositions can neither be both true together nor both false together? Choose the correct answer from the options given below.
- 1. All squares are rectangles
- 2. Some squares are rectangles
- 3. No squares are rectangles
- 4. Some squares are not rectangles
A1 and 2 only
B2 and 3 only ✓ Correct
C1 and 3 only
D1, 2 and 4 only
Correct answer: (B) 2 and 3 only — Statements 2 and 3 are contradictories, so the answer is 2 and 3.
Explanation
★Statements 2 and 3 are contradictories, so the answer is 2 and 3.
★Two propositions that can neither both be true nor both false are contradictories.
★Statement 2, some squares are rectangles, is a particular affirmative.
★Statement 3, no squares are rectangles, is the universal negative.
★These two are contradictories on the square of opposition.
★So exactly one is true and one is false, meaning statements 2 and 3 fit.
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