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: All trees are flowers. No flower is fruit. All branches are fruits.
Conclusions:
- Some branches are trees.
- No fruit is tree.
- No tree is branch.
All trees are flowers. No flower is fruit.
Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and should not contain the middle term. So, it follows that 'No tree is fruit'. II is the converse of this conclusion and so it follows.
All branches are fruits. No flower is fruit.
Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and should not contain the middle term. So, it follows that 'No branch is flower'.
All trees are flowers. No branch is tree.
As discussed above, it follows that 'No tree is branch'. So, III follows.
Hence, both II and III follow.
This, along with the first sentence implies "No trees are branches" or "No branches are trees. " This is the same as III. So, we do have a definite conclusion here regarding extreme terms. So, I is always false and III is always true. That is why either option does not hold here.