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

Only one premise is on the table, so no combining is possible. With a single premise the only things that can follow are restatements of it, conversions of it, or weaker versions of it. Anything that adds a fresh fact, or reverses the relationship, is out. Test the options against that rule.

1. No one who has squared a circle is a mathematician: This is the premise in tidy standard form. "One who has squared a circle is not a mathematician" is a general statement about anyone in that description, so spelling it out as "no one who has squared a circle" changes the wording without changing the meaning. Nothing new is claimed, which is why it is safe.
2. All non-mathematicians have squared a circle: This inverts a group membership. Being told that circle squarers land outside the mathematicians group tells you nothing about what the rest of that outside region contains. Bakers, lawyers and cricketers are all non mathematicians who have never squared anything.
3. Some mathematicians have squared a circle: This tries to open an overlap that the premise seals shut. If even one mathematician had squared a circle, the premise would immediately strip him of the title, so the option is self defeating.
4. All mathematicians square a circle: Same collision, only bigger. Applying the premise to every mathematician would empty the group of mathematicians entirely, which no single premise about circle squarers can do.

The useful lesson is about the two directions of a negative statement. "Circle squarers are not mathematicians" can safely be flipped into "mathematicians are not circle squarers", since a universal negative converts freely. What it cannot be flipped into is any statement about non mathematicians in general, which is the trap in option (B).

Let's summarize:

• A single premise supports only its own restatement or conversion.
• Option (A) is the premise written in standard form, so it follows.
• Options (C) and (D) contradict the premise, and option (B) reverses a group membership that was never stated.

So option (A) is correct.