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
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.
