Question

In each of the questions below are given three statements followed by three conclusions numbered, I II and III. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements
Some boxes are hammers.
Some hammers are heads.
All beads are rings.

Conclusions
I. Some rings are hammers.
II. Some hammers are boxes.
III. Some rings are boxes.

• A. None follows
• B. Only I follows
• C. Only II and III follow
• D. Only I and II follow
• E. All follow

Answer 1

The correct option is D Only I and II follow

The first and second premises are particular affirmative (I-type) and the third premise is universal affirmative (A-type).
Some hammers are beads.
All beads are rings.
$I+A\Rightarrow I$-type conclusion
Conclusion, some hammers are rings.
Conclusion I is the converse of this conclusion.
Conclusion II is the converse of the first premise.