The given statement can be shown by the following diagram :
Some rivers are hills + No hill is taxi = I + E = O = Some rivers are not taxis Hence II does not follow. Again, Since O-type statements can't be combined, neither I nor III follows. But the two form a complementary E- I pair, Hence either I or III follows.
All stones are rivers + All rivers are cars = A + A = A = All stones are cars ? conversion ? Some cars are stones (I) Hence II follows. All rivers are cars + Some cars are trains = I + A = No conclusion Hence II and consequently I do not follow.
Some books are trees + All tress are roads = I + A = I = Some books are roads (I) Hence II follows. Some books are trees + All roads are wheels = I + A = I = Some books are wheels ? conversion ? Some wheels are books (I) Hence I follows. All trees are roads + All roads are wheels = A + A = A = All trees are wheels ? conversion ? Some wheels are trees (I) Hence III follows.
Some mirrors are pens + No pen is paper = 1 + E = O* = Some mirrors are not papers Hence III does not follow. All buildings are mirrors + Some mirrors are pens = A + I = No conclusion Hence II and consequently I do not follow.
All windows are doors + All doors are boats = A + A = A = All windows are boats. Hence I follows. All buildings are doors + All doors are boats = A + A = A = All buildings are boats. Hence II follows. All doors are boats (A) ? conversion ? Some boats are doors(I). Hence III follows.
Statement I consists of two Particular Affirmative (I-type) Premises.
Statement II consists of two Universal Affirmative (A-type) Premises.
Some locks are numbers. ? All numbers are letters.
I + A ? I-type of Conclusion "Some locks are letters".
This is Conclusion II.
All numbers are letters. ? All letters are words.
A + A ? A-type of Conclusion "All numbers are words".
Conclusion I is Converse of it.
All professors are learned and learned people are always gentle. So, all professors are gentle persons. It means the Inference is true.
All Majors are captains.
All Majors are Lieutenants.
All Majors are Soldiers.
(This is Conclusion III )
All captains are Soldiers.
(This is Conclusion IV ).
All Lieutenants are Soldiers.
All Painters are Soldiers.
No Painter is Captain.
The first premise is particular Affirmative (I- Type). The second premise is Universal Affirmative (A-Type).
We can align the premises by converting the first premise and changing their order. Thus,
X is poor ? Some poors are peons have a doctorate degree.
We know that,
A + I = No conclusion.
Both the Premises are Universal Affirmative (A-type). We can align the Premises by taking converse of any of the premises.
Some tall men are basketball players ? All basketball players are athletes.
I + A ?I - type of conclusion "Some tall men are athletes".
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