Direction: In the question below are given three statements followed by two conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the given conclusions and then decide which of the following conclusions logically follows from the given statements disregarding commonly known facts. Statements: Some sketch are not creative. All creative are pen. A few sketch are ink. Conclusions: I. Some pen are ink. II. No pen is ink.
Either I and II follows
Analyzing Syllogism Statements: Sketch, Creative, Pen, Ink
This problem involves analyzing logical syllogisms based on given statements and determining which conclusions necessarily follow. We need to evaluate the relationships between the categories: Sketch, Creative, Pen, and Ink.
Understanding the Statements
- Statement 1: Some sketch are not creative.
This means there is at least one 'sketch' that does not belong to the 'creative' category. It implies that the set of sketches and the set of creative things are not identical, and not all sketches are creative.
- Statement 2: All creative are pen.
This statement establishes a subset relationship: the entire 'creative' category is contained within the 'pen' category. If something is creative, it must also be a pen.
- Statement 3: A few sketch are ink.
This indicates an overlap between the 'sketch' category and the 'ink' category. There exists at least one item that is both a sketch and an ink.
Evaluating the Conclusions
We need to check if the conclusions logically follow from the combination of these three statements.
- Conclusion I: Some pen are ink.
This conclusion suggests an overlap between the 'pen' category and the 'ink' category.
- Conclusion II: No pen is ink.
This conclusion suggests that the 'pen' category and the 'ink' category are completely separate, with no common members.
Notice that Conclusion I and Conclusion II are contradictory. They cannot both be true simultaneously; if one is true, the other must be false.
Logical Deduction and Venn Diagrams
Let's use a logical approach, potentially visualized with Venn diagrams:
- From Statement 3, we know there's an intersection between Sketch and Ink (let's call this set SI). SI is not empty.
- From Statement 2, the set Creative (C) is entirely within the set Pen (P). So, C ⊆ P.
- From Statement 1, there's a part of Sketch (S) that is outside Creative (S ∩ ¬C ≠ ∅).
Scenario Check for Conclusion I (Some pen are ink):
Consider the intersection SI (items that are both sketch and ink). Is it possible for these items (or some of them) to also be 'pen'? Yes. If the items in SI happen to also be 'creative', then by Statement 2, they must be 'pen'. In this case, SI would overlap with P, meaning P and I overlap, making Conclusion I true.
Example where I is true: Let S={a,b,c}, C={a}, P={a,d}, I={a,b}. Statements hold: S1(Some S not C - {b,c}), S2(All C in P - {a} in {a,d}), S3(Some S in I - {a,b}). Conclusion I (Some P in I - {a}) is TRUE. Conclusion II (No P in I) is FALSE.
Scenario Check for Conclusion II (No pen is ink):
Is it possible for the intersection SI (sketch and ink) to exist entirely outside the 'pen' category? Yes. Statement 2 only guarantees that 'creative' things are 'pen'. It doesn't say anything about non-creative things. If the sketches that are inks (SI) are also non-creative, they don't necessarily have to be pens. If SI falls entirely outside P, then P and I would have no overlap.
Example where II is true: Let S={b,c}, C={a}, P={a,d}, I={b,c}. Statements hold: S1(Some S not C - {b,c}), S2(All C in P - {a} in {a,d}), S3(Some S in I - {b,c}). Conclusion I (Some P in I) is FALSE. Conclusion II (No P in I) is TRUE.
Conclusion
We have established scenarios consistent with the given statements where Conclusion I is true and Conclusion II is false, and other scenarios where Conclusion II is true and Conclusion I is false.
Because the premises allow for situations where 'Some pen are ink' is true AND situations where 'No pen is ink' is true, and these two conclusions are mutually exclusive, it means that *either* one or the other *could* be true, but we cannot definitively say which one *must* be true based solely on the given statements. Therefore, the relationship between the conclusions is that either I or II follows.
Similar Questions
- Direction: In the question below are given three statements followed by two conclusions numbered I, II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known fact.Statements:All A are B.Some B are C.Some C are D.Conclusions:l. All B are A.ll. All D are C.
Direction: In the question below are given some statements followed by some conclusions. You have to take given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements:
All Machines are Transformers
All Transformers are Motors
Only a few Machines are Generators
Conclusions:
I. Some Generators are Transformers
II. Some Motors are Machines
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.
