In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
Some watches are clocks.
All clocks are black.
All black are big.
Conclusions:
I. Some watches are big.
II. Some watches are black.
Logical Deduction from Statements
The problem involves analyzing three statements and determining which of the two conclusions logically follow. We will use the given statements to establish relationships between the terms: watches, clocks, black, and big.
Statement Analysis
- Statement 1: Some watches are clocks. This means there's an overlap between the set of watches and the set of clocks.
- Statement 2: All clocks are black. This implies the entire set of clocks is contained within the set of black things.
- Statement 3: All black are big. This implies the entire set of black things is contained within the set of big things.
Reasoning for Conclusion II
Conclusion II: Some watches are black.
- From Statement 1, we know 'Some watches are clocks'.
- From Statement 2, we know 'All clocks are black'.
- Combining these, if some watches belong to the 'clocks' category, and all items in the 'clocks' category belong to the 'black' category, then those specific watches must also be black.
- Therefore, 'Some watches are black' logically follows.
Reasoning for Conclusion I
Conclusion I: Some watches are big.
- We have established from the previous step that 'Some watches are black'.
- From Statement 3, we know 'All black are big'.
- If some watches are black, and all black things are big, then those specific watches must also be big.
- Therefore, 'Some watches are big' logically follows.
Final Decision
Since both Conclusion I and Conclusion II logically follow from the given statements, the correct option is the one stating that both conclusions are valid.
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.
