Question

In each of the questions below are given four statements followed by four conclu-sions numbered I, II, Ill and IV. You have to take the given statements to be true even if they seem to be at variance from 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 :
All brands are bottles.
All bottles are machines.
All machines are files.
All files are roots.
Conclusions :
I. Some files are machines.
II. Some brands are roots.
III. Some machines are roots.
IV. All brands are files.

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

Answer 1

The correct option is D All follow

All brands are bottles.
All bottles are machines.
$A+A\Rightarrow A$-type of Conclusion
"All brands are machines."
All bottles are machines.
All machines are files.
$A+A\Rightarrow A$-type of Conclusion
"All bottles are files."
All machines are files.
All files are roots.
$A+A\Rightarrow A$-type of Conclusion
"All machines are roots.
Conclusion III is the Implication of this conclusion.
All brands are machines.
All machines are files.
$A+A\Rightarrow A$-type of Conclusion
"All brands are files."
It is Conclusion IV.
Conclusion I is Converse of the third Premise.
All brands are files
All files are roots.
$A+A\Rightarrow A$-type of Conclusion
"All brands are roots".
Conclusion II is the Implication of this Conclusion.