Question

Statements: Some cats are dogs. All dogs are animals. Conclusions: I. Some cats are animals. II. All cats are animals.

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

Hint:

Draw overlapping circles for the 'some' relationship and a fully enclosing circle for the 'all' relationship, then check whether the entire first circle - or only the overlapping part - is forced inside the third circle.

Answer 1

The Correct Option is A

Step 1: Draw two circles for "cats" and "dogs" that partially overlap, since the statement is "Some cats are dogs" (a particular, not a universal, statement). Draw a third, larger circle for "animals" that completely encloses the entire "dogs" circle, since all dogs are animals.
Step 2: The overlapping region shared by "cats" and "dogs" lies entirely inside the "dogs" circle, which in turn lies entirely inside the "animals" circle. So that same overlapping region is automatically also inside "animals".
Step 3: This means the "cats" circle and the "animals" circle share at least this non-empty region, which is exactly what "Some cats are animals" requires. Conclusion I is valid.
Step 4: For conclusion II ("All cats are animals") to hold, the entire "cats" circle - not just its overlap with "dogs" - would need to sit inside "animals". Because only "some" cats are confirmed to be dogs, the rest of the cats circle can freely extend outside both "dogs" and "animals" without breaking any given statement.
Step 5: Since a valid diagram can be drawn where some cats fall outside the "animals" circle, conclusion II is not guaranteed to follow.
Correct option: Only conclusion I follows