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Question

In the question below some statements are given some conclusions followed by some statements. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read the conclusions and then decide which of the following statement is true for given conclusions.

Conclusions:

I. Some Signs are Symbols.

II. Some Signs are not Marks.

III. No Number is a Mark.

Statements:

A No Sign is a Number. All Numbers are Symbols. Some Symbols are Marks. Correct Answer Incorrect Answer
B Only a few Signs are Numbers. All Numbers are Symbols. No Symbol is a Mark. Correct Answer Incorrect Answer
C Some Marks are Numbers. Some Numbers are Symbols. No Symbol is a Sign. Correct Answer Incorrect Answer
D All Signs are Symbols. All Symbols are Numbers. Only a few Numbers are Marks. Correct Answer Incorrect Answer
E None of these Correct Answer Incorrect Answer

Solution

From Statement I. No Sign is a Number (E) + All Numbers are Symbols (A) → Some Symbols are not Signs (O*). Hence neither conclusion I nor II follow. All Numbers are Symbols (A) + Some Symbols are Marks (I) → No conclusion. Hence conclusion III does not follow.   From Statement II. Only a few Signs are Numbers (I) + All Numbers are Symbols (A) → Some Signs are Symbols (I). Hence conclusion I follows. Only a few Signs are Numbers (I) + All Numbers are Symbols (A) → Some Signs are Symbols (I) + No Symbol is a Mark (E) → Some Signs are not Marks (O). Hence conclusion II follows. All Numbers are Symbols (A) + No Symbol is a Mark (E) → No Number is a Mark (E). Hence conclusion III follows.   From Statement III. No Symbol is a Sign (E) → Conversion → No Sign is a Symbol (E). Hence conclusion I does not follow. Some Marks are Numbers (I) + Some Numbers are Symbols (I) → No conclusion. Hence neither conclusion II nor III follow.   From Statement IV. All Signs are Symbols (A) → I.I. → Some Signs are Symbols (I). Hence conclusion I follows. All Signs are Symbols (A) +   All Symbols are Numbers (A) → All Signs are Numbers (A) + Only a few Numbers are Marks (I) → No conclusion. Hence conclusion II does not follow. Only a few Numbers are Marks → Some Numbers are Marks (I). Hence conclusion III does not follow.

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