Model 1: The question contains a statements followed by two conclusions numbered I and II. Consider 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.
Given:
a) If only conclusion I follows.
b) If only conclusion II follows.
c) If either conclusion I or II follows.
d) If neither conclusion I nor II follows.
e) If both conclusions I and II follows.
Statements:
All vegetables are plants.
No plant is flower.
Some flowers are jungles.
All jungles are trees.
Conclusions:
I: Some trees are plants.
II: no plant is tree.
Solution:
First and fourth are universal affirmative(A - type), Second statement is universal negative (E -type) and third statement is particular affirmative (I - type).
All vegetables are plants ⇒ No plant is flower.
A + E ⇒ E - type conclusion
Therefore, No vegetable is flower.
Now, No plant is flower ⇒ Some flowers are jungles.
E + I ⇒ [latex]O_{1}[/latex] - type conclusion
Therefore, Some jungles are not plants.
Now, Some flowers are jungles ⇒ All jungles are trees.
I + A ⇒ I - type conclusion
Therefore, Some flowers are trees.
Hence, Conclusion I and II form complementary pair.
Therefore, either I or II follows.
Model 2: The question contains a statements followed by two conclusions numbered I and II. Consider 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.
Given:
a) If only conclusion I follows.
b) If only conclusion II follows.
c) If either conclusion I or II follows.
d) If neither conclusion I nor II follows.
e) If both conclusions I and II follows.
Statements:
All cakes are breads.
Some breads are fruits.
Some fruits are biscuits.
All biscuits are snacks.
Conclusions:
I: Some snacks are fruits
II: Some cakes are fruits.
Solution:
First and fourth premises are universal affirmative (A - type).
Second and third premises are particular affirmative (I - type).
Now, Some fruits are biscuits ⇒ All biscuits are snacks.
I + A ⇒ I - type conclusion.
Therefore, Some fruits are snacks.
Conclusion I is converse of this conclusion.
Therefore, only conclusion I follows.
Model 3: The question contains a statements followed by two conclusions numbered I and II. Consider 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.
Given:
a) None follows.
b) Only I and II follows.
c) Only II and III follows.
d) Only I and III follows.
e) All follows.
Statements:
All tables are boards.
All pens are boards.
All boards are papers.
Conclusions:
I: Some pens are tables.
II: Some papers are pens.
III: No pen is table.
Solution:
All the three premises are universal affirmative (A - type).
Now, All pens are boards ⇒ All boards are papers.
Hence, A + A ⇒ A - type conclusion.
Therefore, All pens are papers.
Conclusion II is converse to this conclusion.
Now, All tables are boards ⇒ All boards are papers.
Hence, All tables are papers.
Conclusions I and III form complementary pair.
Therefore, either conclusion I or III follows.
Model 4: The question contains a statements followed by two conclusions numbered I and II. Consider 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.
Given:
a) None follows.
b) Only I and II follows.
c) Only II and III follows.
d) Only I and III follows.
e) All follows.
Statements:
All jackets are trousers.
No trouser is shirt.
Some shirts are caps.
Conclusions:
Solution:
First premise is universal affirmative (A - type).
Second premise is universal negative (E - type).
Third is particular affirmative (I - type)
Now, All jackets are trousers ⇒ No trouser is shirt.
hence, A + E ⇒ E - type.
Conclusion is Sopme caps are not trousers.
Conclusion III is converse of the first.
Therefore, Only II and III follows.
Model 5: The question contains a statements followed by two conclusions numbered I and II. Consider 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.
Given:
a) None follows.
b) Only I and II follows.
c) Only II and III follows.
d) Only I and III follows.
e) All follows.
Statements:
Some tents are buildings.
Some buildings are chairs.
Some chairs are windows.
Conclusions:
I: Some windows are buildings
II: Some windows are tents.
III: Some chairs are tents.
Solution:
Given
Some windows are buildings, Some windows are tents and Some chairs are tents.
No conclusion follows from particular premises.
Hence, only conclusion I follows.