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. 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 flats are villas.
No villa is an apartment.
Conclusions:
(I) No flat is an apartment.
(II) No apartment is a villa. - 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 pins are bugs.
All pins are cows.
Conclusions:
(I): Some bugs are cows.
(II): All cows are pins. 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 conclusions logically follow(s) from the statement(s).
Statement:
Most students know English language.
Conclusions:
1. Some students know English language.
2. Some students do not know English language.
- Two statements are given below. Decide which of the options logically follow from these statements.
Statement 1 All bags are toys.
Statement 2: Some toys are suitcases. - 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 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 conclusion(s) logically follow(s) from the statements.
Statements: All kiwis are bananas. All bananas are grapes.
Conclusions (I): All kiwis are grapes.
Conclusions (II): Some grapes are bananas.
Important Questions from Syllogism
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 dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
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 directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
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:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
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 employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
