Logical Reasoning - Logical Deduction - Discussion
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 the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some uniforms are covers. All covers are papers. All papers are bags.
Conclusions:
- All covers are bags.
- Some bags are covers, papers and uniforms.
- Some uniforms are not papers.
Some uniforms are covers. All covers are papers.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some uniforms are papers'. All covers are papers. All papers are bags.
Since both the premises are universal and affirmative, the conclusion must be universal affirmative (A-type) and should not contain the middle term. So, it follows that 'All covers are bags'. Thus, I follows. The converse of this conclusion i.e. 'Some bags are covers' also holds.
Some uniforms are covers. All covers are bags.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some uniforms are bags', The converse of this conclusion i.e. 'Some bags are uniforms' also holds.
Further, the converse of the third premise i.e. 'Some bags are papers' holds.
Now, II is the cumulative result of the conclusions 'Some bags are covers', 'Some bags are papers' and 'Some bags are uniforms'. Thus, II follows.
So why is the D option wrong?
If a part of uniforms is covers and that part (covers and uniforms) is papers and so on, there is a part of uniforms that's not covers, papers, or bags.
Assume a case, where some uniforms are covers. All covers are papers, and rest all uniforms are papers. So basically uniforms are covers and papers, but all covers are papers, hence all uniforms are papers.
In this case; Option D does not hold true, owing to the uncertainty of association of remaining uniforms.