Neither l nor ll follows
Logical Reasoning: Analyzing Syllogism Statements and Conclusions
This question tests our ability to logically deduce conclusions from given statements. We need to determine if the conclusions necessarily follow from the premises, disregarding any real-world knowledge.
Understanding the Given Statements
Let's break down the statements provided:
- Statement 1: All A are B. This means the entire set 'A' is included within the set 'B'. Symbolically, this can be represented as '$A \subseteq B$'.
- Statement 2: Some B are C. This indicates that there is at least one member that belongs to both set 'B' and set 'C'. The intersection of B and C is not empty. Symbolically, '$B \cap C \neq \emptyset$'.
- Statement 3: Some C are D. Similarly, this means there is at least one member that belongs to both set 'C' and set 'D'. The intersection of C and D is not empty. Symbolically, '$C \cap D \neq \emptyset$'.
Analyzing Conclusion I: All B are A
The conclusion states: All B are A. Symbolically, '$B \subseteq A$'.
Statement 1 tells us that 'All A are B' ($A \subseteq B$). This implies that A is a subset of B. However, it does not provide any information about whether B is a subset of A. It's possible for B to contain elements that are not in A. For example, if A represents 'Dogs' and B represents 'Mammals', the statement 'All Dogs are Mammals' is true, but the conclusion 'All Mammals are Dogs' is false. Therefore, Conclusion I does not logically follow from the given statements.
Analyzing Conclusion II: All D are C
The conclusion states: All D are C. Symbolically, '$D \subseteq C$'.
Statement 3 tells us that 'Some C are D' ($C \cap D \neq \emptyset$). This means that there is an overlap between sets C and D; at least one element is common to both. However, this statement does not guarantee that the entire set D is contained within set C. It only confirms a partial overlap. There might be elements in D that are not in C. For instance, if C represents 'Students who like Maths' and D represents 'Students who like Physics', the statement 'Some students who like Maths also like Physics' might be true, but it doesn't mean 'All students who like Physics also like Maths'. Therefore, Conclusion II does not logically follow from the given statements.
Final Deduction
Since neither Conclusion I ('All B are A') nor Conclusion II ('All D are C') is a necessary logical consequence of the provided statements, we conclude that neither conclusion follows.
The correct option is the one stating that neither I nor II follows.
Similar Questions
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.
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.
