Question

Instructions (133 to 135): Select the statement which logically follows the two given statements.

Statement:
I One who has squared a circle is not a mathematician
II Therefore ----------------------

• A. No one who has squared a circle is a mathematician
• B. All non-mathematicians have squared a circle
• C. Some mathematicians have squared a circle
• D. All mathematicians square a circle

Hint:

Only one statement is given, so look for the option that says the same thing in cleaner wording rather than one that adds a new fact.

Answer 1

The Correct Option is A

Step 1: Understanding the Question.
Only one statement is given here. It says that a person who has squared a circle is not a mathematician. We must pick the statement that follows from it.

Step 2: Key Formula or Approach.
The phrase "one who" in this kind of sentence is a general claim, not a claim about a single named person. It means anyone at all who has squared a circle fails to be a mathematician. Rewritten in standard form, the statement is "No person who has squared a circle is a mathematician". A restatement in standard form always follows, since it says exactly the same thing in different words.

Step 3: Detailed Explanation.
Option (A) is that standard form restatement. It keeps both terms in the same roles and keeps the negative link intact. It adds nothing and drops nothing, so it follows.
As background, squaring the circle is a construction that geometry has proved impossible with compass and straightedge, so the group of people who have squared a circle is a group nobody can actually join. That is the joke behind the question, but the logic does not depend on it.

Step 4: Checking the Wrong Options.
Option (B) says all non mathematicians have squared a circle. The statement only tells us that circle squarers are non mathematicians. It never claims the reverse, that every non mathematician is a circle squarer. Most non mathematicians have never attempted the construction at all.
Option (C) says some mathematicians have squared a circle. This directly contradicts the given statement, which keeps mathematicians and circle squarers apart completely. A conclusion may never contradict its premise.
Option (D) says all mathematicians square a circle. This too collides head on with the statement. If a mathematician squared a circle, then by the premise he would not be a mathematician, which is absurd.

Step 5: Final Answer.
The statement in proper form is that no circle squarer is a mathematician, so the answer is (A).