Three statements are given, followed by three conclusions numbered I, II and III. 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: All Cadbury are Nestle. No Nestle is Amul. Some Cadbury are Britannia. Conclusions: I. Some Nestle are Britannia. II. No Amul is a Cadbury III .No Amul is Britannia.
Only conclusions I and II follow
Analyzing Syllogism Statements and Conclusions
This problem requires us to analyze logical statements and determine which conclusions logically follow based on the principles of syllogism. We are given three statements and three conclusions related to different brands: Cadbury, Nestle, Amul, and Britannia.
Given Statements:
- All Cadbury are Nestle.
- No Nestle is Amul.
- Some Cadbury are Britannia.
Statement Analysis and Representation
Let's break down what each statement tells us:
- Statement 1: All Cadbury are Nestle. This means that the set of 'Cadbury' is completely included within the set of 'Nestle'.
- Statement 2: No Nestle is Amul. This indicates that the set of 'Nestle' and the set of 'Amul' have no overlap. They are mutually exclusive. Since 'All Cadbury are Nestle', this also implies that no Cadbury can be Amul.
- Statement 3: Some Cadbury are Britannia. This tells us there is at least one element (or item) that is both 'Cadbury' and 'Britannia'. This shows an overlap between the 'Cadbury' set and the 'Britannia' set.
We can visualize these relationships using Venn diagrams:
- A circle for Cadbury is inside a circle for Nestle.
- A circle for Amul is drawn completely separate from the Nestle circle.
- A circle for Britannia overlaps with the Cadbury circle. The overlap area represents 'Some Cadbury are Britannia'. Since the Cadbury circle is inside the Nestle circle, this overlap area is also necessarily inside the Nestle circle.
Evaluating the Syllogism Conclusions
Now, let's examine each conclusion based on the given statements and our understanding of their relationships.
Conclusion I: Some Nestle are Britannia.
We know from Statement 3 that 'Some Cadbury are Britannia'. From Statement 1, we know that 'All Cadbury are Nestle'. Since all Cadbury items are also Nestle items, and some Cadbury items are Britannia items, the items that are both Cadbury and Britannia must also be Nestle. Therefore, there are items that are both Nestle and Britannia. This conclusion logically follows from the statements.
Conclusion II: No Amul is a Cadbury.
Statement 2 says 'No Nestle is Amul'. Statement 1 says 'All Cadbury are Nestle'. If the entire set of Nestle has no overlap with Amul, and the entire set of Cadbury is contained within Nestle, then there cannot be any overlap between Cadbury and Amul. If something is a Cadbury, it must be a Nestle, and if it's a Nestle, it cannot be an Amul. Therefore, no Amul can be a Cadbury. This conclusion logically follows from the statements.
Conclusion III: No Amul is Britannia.
We know 'No Nestle is Amul' (Statement 2) and 'Some Cadbury are Britannia' (Statement 3), and 'All Cadbury are Nestle' (Statement 1). We established that 'No Amul is Cadbury' (Conclusion II). However, the statements do not provide a direct relationship between Amul and Britannia. While the part of Britannia that is Cadbury cannot be Amul, the statements don't preclude the possibility of Amul having an overlap with the part of Britannia that is *not* Cadbury (if such a part exists). We cannot definitively conclude that 'No Amul is Britannia' based solely on the given statements. Therefore, this conclusion does not necessarily follow.
Summary of Syllogism Conclusion Analysis
Based on the analysis:
- Conclusion I (Some Nestle are Britannia) follows.
- Conclusion II (No Amul is a Cadbury) follows.
- Conclusion III (No Amul is Britannia) does not necessarily follow.
Therefore, only conclusions I and II logically follow from the given statements.
Revision Table: Syllogism Rules and Types
| Statement Type | Quantifier | Example | Relationship |
|---|---|---|---|
| Universal Affirmative (A) | All | All A are B | Set A is subset of Set B |
| Universal Negative (E) | No | No A is B | Sets A and B are disjoint |
| Particular Affirmative (I) | Some | Some A are B | Sets A and B have overlap |
| Particular Negative (O) | Some...not | Some A are not B | Set A has elements outside of Set B |
Additional Information: Understanding Syllogism Validity
Syllogism is a form of deductive reasoning where a conclusion is derived from two or more propositions (statements). A conclusion is considered 'valid' if it logically follows from the premises (statements), regardless of whether the premises themselves are factually true in the real world. In this problem, we assumed the statements to be true and checked for logical validity of the conclusions.
Key points in Syllogism:
- Premises: The statements given.
- Conclusion: The statement that is deduced from the premises.
- Validity: A syllogism is valid if the conclusion must be true whenever the premises are true.
- Truth: Refers to whether a statement corresponds to reality. Syllogism focuses on validity, not necessarily truth.
Methods like Venn diagrams or standard syllogism rules can be used to determine validity. The question asks which conclusions logically follow, which is about validity based on the provided statements.
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.
