Question

Statements: All pens are books. All books are tables. Conclusions: I. All pens are tables. II. Some tables are pens.

• A. Only conclusion I follows
• B. Only conclusion II follows
• C. Both conclusions I and II follow
• D. Neither conclusion follows

Hint:

Sketch the three categories as one circle fully inside another fully inside a third, and see what that nesting forces about overlap between the outermost and innermost circles.

Answer 1

The Correct Option is C

Step 1: Draw three nested circles: the "pens" circle sits completely inside the "books" circle (since all pens are books), and the "books" circle sits completely inside the "tables" circle (since all books are tables).
Step 2: Because circles are nested inside one another, the innermost "pens" circle automatically lies completely inside the outermost "tables" circle as well. This directly means every pen is a table, so conclusion I ("All pens are tables") is valid.
Step 3: Now look at the overlap between the "tables" circle and the "pens" circle. Since the entire non-empty "pens" circle lies inside "tables", the shared region between them is exactly the whole "pens" circle, which is not empty.
Step 4: A non-empty shared region between "tables" and "pens" is precisely what the statement "Some tables are pens" requires, so conclusion II is also valid.
Step 5: Since both nested-circle checks succeed, neither conclusion can be rejected.
Correct option: Both conclusions I and II follow