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
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.
