Question

Question:
The question given below has two statements followed by three conclusions. By assuming the statements are true, find out from the given conclusions which of the conclusions is logically correct.

Statements:
(i) All doors are tables.
(ii) No tables are chairs.

Conclusions:
I. No doors are chairs.
II. No chairs are doors.
III. Some tables are doors.

Answer Options:
(1) Only I and II
(2) Only II and III
(3) All three
(4) None of these

Answer 1

Step-by-Step Explanation:

Analyze the Statements:

All doors are tables:

This means every door is a table, but not all tables are necessarily doors.

Diagrammatically:

No tables are chairs:

This means there is no overlap between tables and chairs.

Diagrammatically:

Evaluate the Conclusions:

No doors are chairs:

From the statements, all doors are tables, and no table is a chair. Hence, no door can be a chair.

Conclusion I is correct.

No chairs are doors:

Since no door is a chair (as shown above), it follows logically that no chair is a door.

Conclusion II is correct.

Some tables are doors:

From Statement 1, all doors are tables. This implies that some tables are indeed doors (all doors belong to the subset of tables).

Conclusion III is correct.

Final Answer:

(3) All three

All the conclusions (I, II, and III) are logically correct based on the given statements.