Which of the following statements are logically equivalent? A. All pens are…
2026
Which of the following statements are logically equivalent?
A. All pens are non-pencils.
B. All non-pencils are pens.
C. No pencils are pens.
D. No pens are pencils.
Choose the correct answer from the options given below:
- A.
B and D Only
- B.
A and B Only
- C.
B, C and D Only
- D.
A, C, and D Only
Attempted by 14 students.
Show answer & explanation
Correct answer: D
Statements A, C, and D are logically equivalent because they all express the universal negative proposition that no pens are pencils.
Statement A (All pens are non-pencils) is equivalent to No pens are pencils (Statement D).
Statement C (No pencils are pens) is the converse and also equivalent.
Statement B claims all non-pencils are pens, which is a different logical relationship.