Three statements are given, followed by three conclusions numbered 1, 2 and 3. Assuming the statements to be true, even if they seem to be at variance with known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All folders are copies.
All books are folders.
No copies are pen.
Conclusions:
No book is a pen.
All books are copies.
Some copies are books.
- AOnly conclusions 1 and 3 follow
- BAll conclusions follow
- COnly conclusions 1 and 2 follow
- DOnly conclusions 2 and 3 follow
Solution & Step-by-step Explanation
Let's analyze using standard set relations:
From statements: Books⊂Folders⊂Copies.
Also, Copies∩Pen=∅.
Let's evaluate the conclusions:
No book is a pen: Since all books are inside copies, and no copy can be a pen, no book can be a pen either. This conclusion is true.
All books are copies: Since Books⊂Folders and Folders⊂Copies, it follows directly that all books are copies. This conclusion is true.
Some copies are books: Since books are a subset of copies, the region occupied by books represents some part of copies. This conclusion is true.
Therefore, all conclusions follow.
From statements: Books⊂Folders⊂Copies.
Also, Copies∩Pen=∅.
Let's evaluate the conclusions:
No book is a pen: Since all books are inside copies, and no copy can be a pen, no book can be a pen either. This conclusion is true.
All books are copies: Since Books⊂Folders and Folders⊂Copies, it follows directly that all books are copies. This conclusion is true.
Some copies are books: Since books are a subset of copies, the region occupied by books represents some part of copies. This conclusion is true.
Therefore, all conclusions follow.