In this question, three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusion(s) logically follow(s) from the statements.
Statements:
All chairs are tables.
Some tables are stands.
All stands are baskets.
Conclusions:
I. Some chairs are stands.
II. Some tables are baskets.
III. All baskets are chairs.
- AOnly conclusions II and III follow.
- BOnly conclusion II follows.
- COnly conclusions I and II follow.
- DOnly conclusion III follows.
Solution & Step-by-step Explanation
Let's evaluate each conclusion using Venn diagrams or logical deduction:
Statement analysis:
All chairs are tables. (Chairs ⊆ Tables)
Some tables are stands. (Tables ∩ Stands
=∅)
All stands are baskets. (Stands ⊆ Baskets)
Evaluating Conclusions:
Conclusion I: "Some chairs are stands." There is no definite intersection given between chairs and stands. Thus, it does not logically follow.
Conclusion II: "Some tables are baskets." Since some tables are stands, and all stands are inside baskets, that overlapping region of tables and stands must also be inside baskets. Hence, some tables are definitely baskets. This conclusion follows.
Conclusion III: "All baskets are chairs." This is clearly not supported by the premises as baskets can be entirely outside chairs. Thus, it does not follow.
Therefore, only conclusion II follows.
Statement analysis:
All chairs are tables. (Chairs ⊆ Tables)
Some tables are stands. (Tables ∩ Stands
=∅)
All stands are baskets. (Stands ⊆ Baskets)
Evaluating Conclusions:
Conclusion I: "Some chairs are stands." There is no definite intersection given between chairs and stands. Thus, it does not logically follow.
Conclusion II: "Some tables are baskets." Since some tables are stands, and all stands are inside baskets, that overlapping region of tables and stands must also be inside baskets. Hence, some tables are definitely baskets. This conclusion follows.
Conclusion III: "All baskets are chairs." This is clearly not supported by the premises as baskets can be entirely outside chairs. Thus, it does not follow.
Therefore, only conclusion II follows.