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. Statements: Some apartments are bungalows. Some bungalows are flats. Conclusions: I. Some apartments are flats. II. Some flats are bungalows.
Only conclusion II follows
Analyzing Statements and Conclusions in Syllogism
This question asks us to analyze the given statements and determine which of the conclusions logically follow from them, assuming the statements are true.
Statements:
- Some apartments are bungalows.
- Some bungalows are flats.
Conclusions:
- Some apartments are flats.
- Some flats are bungalows.
Step-by-Step Analysis:
Analyzing Statement 1: "Some apartments are bungalows."
This statement tells us there is an overlap between the set of 'apartments' and the set of 'bungalows'. There exists at least one apartment that is also a bungalow, and vice versa.
Analyzing Statement 2: "Some bungalows are flats."
This statement tells us there is an overlap between the set of 'bungalows' and the set of 'flats'. There exists at least one bungalow that is also a flat, and vice versa.
We can visualize these relationships using Venn diagrams or think about the connections between the terms.
Analyzing Conclusion I: "Some apartments are flats."
This conclusion tries to establish a direct relationship between 'apartments' and 'flats'. The statements link 'apartments' to 'bungalows' and 'bungalows' to 'flats'. However, just because apartments share something with bungalows (some are bungalows) and bungalows share something with flats (some are flats), it does not automatically mean that apartments must share something with flats. The overlap between apartments and bungalows might be completely separate from the overlap between bungalows and flats.
For example, imagine:
| Category | Items |
|---|---|
| Apartments | A1, A2, A3, A4 |
| Bungalows | B1, B2, B3, B4 |
| Flats | F1, F2, F3, F4 |
Let's say:
- Some apartments are bungalows: A1 is a bungalow (A1 = B1).
- Some bungalows are flats: B4 is a flat (B4 = F1).
In this scenario, A1 is a bungalow, and B4 is a flat, but there is no necessary link shown between apartments and flats. A1 is an apartment and B1 is a bungalow. B4 is a bungalow and F1 is a flat. If B1 and B4 are different bungalows, there is no overlap between apartments and flats. Therefore, Conclusion I does not logically follow.
Analyzing Conclusion II: "Some flats are bungalows."
This conclusion is about the relationship between 'flats' and 'bungalows'. Look back at the statements. Statement 2 explicitly says, "Some bungalows are flats." If it is true that "Some bungalows are flats", it must also be true that "Some flats are bungalows." This is a direct implication of the statement itself. The relationship is reciprocal for 'Some' statements.
If there is an overlap between the set of bungalows and the set of flats, then items in that overlap belong to both sets. So, if some bungalows are flats, then those specific items are both bungalows and flats, meaning some flats are also bungalows.
Therefore, Conclusion II logically follows from Statement 2.
Summary of Conclusions:
- Conclusion I: Some apartments are flats. (Does NOT follow)
- Conclusion II: Some flats are bungalows. (DOES follow)
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.
