Three statements are given followed by two conclusions numbered 1 and 2. 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:
No red is black.
All blues are black.
No blue is pink.
Conclusions:
1. No blue is red.
2. No red is pink.
Logical Reasoning Solution
This question involves analyzing logical statements to determine which conclusions necessarily follow. We will use a step-by-step approach to evaluate each conclusion based on the given statements.
Statements Analysis
- Statement 1: No red is black.
- Statement 2: All blues are black.
- Statement 3: No blue is pink.
Conclusion 1 Evaluation
We need to determine if "No blue is red" logically follows.
- From Statement 2, we know that the set of 'blues' is entirely contained within the set of 'black' items. (Blue ⊆ Black)
- From Statement 1, we know that the set of 'red' items has no overlap with the set of 'black' items. (Red ∩ Black = ∅)
- Since all 'blues' are 'black', and no 'red' item is 'black', it logically follows that no 'blue' item can be a 'red' item.
Therefore, Conclusion 1 logically follows.
Conclusion 2 Evaluation
We need to determine if "No red is pink" logically follows.
- Statement 1 states: No red is black (Red ∩ Black = ∅).
- Statement 3 states: No blue is pink (Blue ∩ Pink = ∅).
- Statement 2 states: All blues are black (Blue ⊆ Black).
The statements establish relationships between red and black, and between blue and pink. However, they do not provide any direct or indirect link between the set 'red' and the set 'pink'. The fact that 'red' is separate from 'black', and 'blue' (which is a subset of 'black') is separate from 'pink', does not logically prevent 'red' and 'pink' from having an overlap, being separate, or one containing the other. No information in the statements allows us to conclude definitively that "No red is pink".
Therefore, Conclusion 2 does not logically follow.
Final Verdict
Based on the analysis, only Conclusion 1 logically follows from the given 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.
