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
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
