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Which of the following statements are logically equivalent?A. No soaps are writing—tools.B. All soaps are non-writing—tools.C. No non—writing—tools ar
Question

Which of the following statements are logically equivalent?
A. No soaps are writing—tools.
B. All soaps are non-writing—tools.
C. No non—writing—tools are soaps.
D. No writing-tools are soaps.
Choose the correct answer from the options given below:

A.

A and D Only

B.

A, B and D Only

C.

B and C Only

D.

A and C Only

Correct option is B

Introduction:

The question requires determining which statements are logically equivalent. Let's analyse each statement to identify any equivalences.
Information Booster:

  • A. No, soaps are writing-tools: This statement implies that soaps and writing-tools are mutually exclusive.
  • B. All soaps are non-writing tools: This statement is equivalent to A, as it also implies that soaps are not writing-tools.
  • C. No non-writing-tools are soaps: This statement is not equivalent to A or B. It implies that all soaps must be writing-tools, which contradicts A and B.
  • D. No writing-tools are soaps: This statement is equivalent to A, as it also implies that writing-tools and soaps are mutually exclusive.
Additional Knowledge:
Logically equivalent statements convey the same meaning, even if they are worded differently. In this case, statements A and D are logically equivalent, as they both imply that soaps and writing-tools do not overlap. Statement B is also logically equivalent to A and D, as it conveys the same meaning differently.
The logically equivalent statements are:

  • A. No soaps are writing-tools
  • B. All soaps are non-writing-tools
  • D. No writing-tools are soaps
These three statements convey the same meaning and are logically equivalent.

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