Below are given statements followed by two conclusions I and II. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. II. All ladies are aunts.
Statements: A: All mothers are aunts.
B: All aunts are ladies.
Conclusions: I. All ladies are mothers
Decide which of the below options logically follows the given Statement.
Analyzing Statements and Conclusions
We are given two statements and two conclusions, and we need to determine which conclusion logically follows from the statements.
Statements:
- Statement A: All mothers are aunts. (Symbolically: $M \rightarrow A$)
- Statement B: All aunts are ladies. (Symbolically: $A \rightarrow L$)
Conclusions:
- Conclusion I: All ladies are mothers. (Symbolically: $L \rightarrow M$)
- Conclusion II: All ladies are aunts. (Symbolically: $L \rightarrow A$)
Logical Deduction from Statements
Using the principle of syllogism, we can combine the given statements:
- From Statement A ($M \rightarrow A$) and Statement B ($A \rightarrow L$), we can deduce that all mothers are ladies ($M \rightarrow L$).
This means the set of 'mothers' is a subset of 'aunts', and the set of 'aunts' is a subset of 'ladies'. Therefore, the set of 'mothers' must be a subset of 'ladies'.
Evaluating Conclusion I
Conclusion I states: All ladies are mothers ($L \rightarrow M$).
Our deduction from the statements is that All mothers are ladies ($M \rightarrow L$). The conclusion $L \rightarrow M$ is the converse of our deduction. The converse of a universal affirmative statement does not necessarily hold true. For example, while all dogs are mammals, it is not true that all mammals are dogs.
Therefore, Conclusion I does not logically follow.
Evaluating Conclusion II
Conclusion II states: All ladies are aunts ($L \rightarrow A$).
From Statement B, we know that All aunts are ladies ($A \rightarrow L$). This implies that the set of aunts is a subset of the set of ladies. Conclusion II states the reverse, that the set of ladies is a subset of the set of aunts ($L \rightarrow A$). This is not supported by the given statements.
Therefore, Conclusion II does not logically follow.
Final Decision
Since neither Conclusion I nor Conclusion II logically follows from the given statements, the correct option is that neither conclusion follows.
Similar Questions
- Read the given statement(s) and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statement(s).
Statements:
All Hummingbirds are Storks.
Some Storks are Flamingos.
Conclusions:
I. Some Hummingbirds are Flamingos.
II. No Flamingos are Hummingbirds. - Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All fathers are brothers.
All brothers are sons.
Conclusions:
(I) All fathers are sons.
(II) All brothers are fathers. - Read the given statements and conclusions carefully and decide which of the conclusions logically follow(s) from the statements.
Statements:
(i) All ships are boats.
(ii) All anchors are ships.
Conclusions:
I. All anchors are boats.
II. Some ships are anchors.
III. No anchor is boat.
IV. Some boats are anchors. Read the given statements and decide which of the conclusions given in the options logically follow from the statements.
Statements:
1. All kitchens are bedrooms.
2. No bedroom is a hall.
Read the given statements and decide which of the conclusions given in the options logically follow from the statements.
Statements:
1. All guitars are instruments.
2. All instruments are bagpipes.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some balls bounce.
All balls vibrate.
Conclusions:
I. Even the balls that do not bounce, vibrate.
II. The balls that do not bounce, do not necessarily vibrate.- Read the given statement(s) and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statement(s).
Statements:
All Wolves are Rhinoceroses.
No Rhinoceroses are Kangaroos.
Conclusions:
I: No Kangaroos are Wolves.
II: Some Kangaroos are Wolves. - Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All doors are carpets.
No carpet is a mat.
Conclusions:
(I) No door is a mat.
(II) No mat is a carpet. - Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follows from the statements.
Statements:
1. Some kiwis are green.
2. Some apples are kiwis.
Conclusions:
1. Some kiwis are yellow.
2. An apple is green. - Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow from the statements.
Statements:
1. All red are white.
2. All white are black.
Conclusions:
1. Some white are red.
2. Some black are red.
3. Some red are not black.
4. All black are white.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
