Which of the following statements are logically equivalent to the statement "Some professors are spiritualists"?
A. Some spiritualists are professors.
B. Some non-spiritualists are not non-professors.
C. No spiritualists are professors.
D. Some professors are not non spiritualists.
Choose the correct answer from the options given below:
- AOption (a)
A, B & D only
- BOption (b)
A & D only
- COption (c)
B & C only
- DOption (d)
C & D only
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Correct answer
A & D only
Why this answer is correct
The correct answer is: A & D only
Important Points
The given statement is "Some professors are spiritualists". This implies that there is at least one professor who is also a spiritualist.
A. Some spiritualists are professors.
- This statement is logically equivalent because it implies the same as the given statement, just reversing the terms.
- It means that there is at least one spiritualist who is a professor..
D. Some professors are not non-spiritualists.
- The double negative here simplifies to "Some professors are spiritualists", which is exactly the same as the original statement.
Therefore, options A and D are logically equivalent to the original statement.
Additional Information
B. Some non-spiritualists are not non-professors.
- This statement might seem a bit tricky because of the double negatives, but it simplifies to "Some non-spiritualists are professors", which isn't equivalent to the original statement
C. No spiritualists are professors.
- This statement is the opposite of the original statement. It contradicts the original statement, saying that there are no professors who are spiritualists.