Which of the following statements is logically equivalent to the statement - "All women are honest human beings"
No women are non-honest human beings.
To determine the logically equivalent statement to "All women are honest human beings", we need to understand the logical structure and possible equivalent statements.
The statement "All women are honest human beings" can be represented logically as:
- If someone is a woman, then they are an honest human being.
This can be expressed in logical terms as:
- If \(W(x)\Rightarrow H(x)\)
Now, let's evaluate each option to see which one is logically equivalent:
- Some women are non-honest human beings.
This statement contradicts the original statement because if some women are non-honest, it negates the idea that all women are honest. - Some honest human beings are women.
This statement introduces the possibility of honest human beings being women but doesn't cover all cases, thus, it is not equivalent. - Some women are honest human beings.
This statement is true but not equivalent because it claims only some women are honest, which is a weaker position than "all". - No women are non-honest human beings.
This is logically equivalent because if there are no non-honest women, it implies that all women must be honest.
Therefore, the correct answer is "No women are non-honest human beings", which is logically equivalent to "All women are honest human beings".
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