Which of the following propositions are logically equivalent to 'No women are dishonest human beings'?
1.No dishonest human beings are women
2.All women are non-dishonest human beings
3.No women are non-dishonest human beings
4.All non-women are non-dishonest
A1 & 2 only ✓ Correct
B3 & 4 only
C1 & 3 only
D1, 2 & 3 only
Correct answer: (A) 1 & 2 only
Explanation
The equivalents are the converse and the obverse of the E proposition.
Starting from 'No women are dishonest human beings,' conversion of an E proposition gives 'No dishonest human beings are women,' which is Statement 1.
Obversion changes the quality to affirmative and replaces the predicate with its complement, giving 'All women are non-dishonest human beings,' Statement 2.
Both operations are truth preserving for the universal negative, so each yields a proposition logically equivalent to the original.
Only conversion and obversion of E hold here, fixing Statements 1 and 2.
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