Two 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 follow(s) from the statements. Statement I: Some musicians are guitarists. Statement II: All guitarists are performers. Conclusion I: Some performers are guitarists. Conclusion II: Some musicians are not performers.
Analyzing the Statements
We are given two statements and need to determine which conclusions logically follow.
- Statement I: Some musicians are guitarists. This means there is an overlap between the set of musicians (M) and the set of guitarists (G). Represented as: $M ∩ G ≠ ∅$.
- Statement II: All guitarists are performers. This means the entire set of guitarists (G) is contained within the set of performers (P). Represented as: $G ⊆ P$.
Evaluating Conclusion I
Conclusion I: Some performers are guitarists. ($P ∩ G ≠ ∅$)
- From Statement II, we know that all guitarists are performers ($G ⊆ P$).
- This directly implies that the set of performers includes all guitarists.
- If there exist guitarists (which is implied by Statement I), then there must exist performers who are also guitarists.
- Therefore, Conclusion I logically follows from Statement II.
Evaluating Conclusion II
Conclusion II: Some musicians are not performers. ($M ∩ ¬P ≠ ∅$)
- Statement I tells us about musicians who ARE guitarists.
- Statement II tells us these guitarist-musicians ARE performers.
- However, the statements provide no information about musicians who are NOT guitarists.
- It is possible that all musicians are performers, or only some are. We cannot be certain based solely on the given statements.
- Therefore, Conclusion II does not necessarily follow.
Final Verdict
Based on the analysis, only Conclusion I is logically 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.
