Which of the following propositions are logically equivalent to ‘No women are dishonest human beings’:
A. No dishonest human beings are women
B. All women are non-dishonest human beings
C. No women are non-dishonest human being
D. All non-women are non-dishonest
Choose the correct answer from the options given below:

Correct option is A

The correct answer is A and B only.
· Proposition A: "No dishonest human beings are women" is the contrapositive of "No women are dishonest human beings." A contrapositive statement is logically equivalent to the original statement, which makes this proposition correct.
· Proposition B: "All women are non-dishonest human beings" is a restatement of the original proposition in positive terms. Instead of saying that no women are dishonest, it affirms that all women are honest (non-dishonest), making it logically equivalent.
· Proposition C: "No women are non-dishonest human beings" is incorrect because it contradicts the original proposition by suggesting that women are dishonest, which is the opposite of the given statement.
· Proposition D: "All non-women are non-dishonest" is irrelevant because it shifts focus to non-women and makes an unrelated statement.
Information Booster:
1. Contrapositive: A statement is logically equivalent to its contrapositive. If "No women are dishonest" is true, then "No dishonest people are women" is also true.
2. Restating in Positive Terms: Rephrasing a negative statement positively can preserve logical equivalence.
3. Misinterpretation: Watch for propositions that flip the meaning, like Proposition C, which contradicts the original statement.
4. Irrelevant Focus: Statements that introduce unrelated groups (like non-women in Proposition D) are not logically equivalent unless they align with the original statement’s logic.