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 crocodiles are tubes.
All tubes are socks.
No sock is a menu.
Conclusions:
(I) Some menus are not socks.
(II) No sock is a crocodile.
(III) Some adapters are houses.
Analyzing the Syllogism: Statements and Conclusions
This problem involves logical reasoning, specifically analyzing syllogisms. We need to determine which conclusions logically follow from the given statements.
Understanding the Statements
Let's break down each statement to understand the relationship between the terms:
- Statement 1: Some crocodiles are tubes. This indicates that there is at least one crocodile that is also a tube. The sets 'crocodiles' and 'tubes' overlap.
- Statement 2: All tubes are socks. This means the entire set of 'tubes' is included within the set of 'socks'. Anything that is a tube is automatically a sock.
- Statement 3: No sock is a menu. This establishes a complete separation between the set of 'socks' and the set of 'menus'. They share no common members. This statement also implies that no menu is a sock.
Combining Information from Statements
By combining the statements, we can infer additional relationships:
- From Statement 1 (Some crocodiles are tubes) and Statement 2 (All tubes are socks), we can logically conclude that some crocodiles are socks. The crocodiles that belong to the 'tubes' category must also belong to the 'socks' category.
- Statement 3 clearly states that the categories 'socks' and 'menus' are mutually exclusive. Using set notation, if $S$ represents the set of socks and $M$ represents the set of menus, then $S \cap M = \emptyset$.
Evaluating the Conclusions
Evaluating Conclusion I: Some menus are not socks
Statement 3 tells us "No sock is a menu", which is logically the same as "No menu is a sock". This means the sets M (menus) and S (socks) are disjoint ($M \cap S = \emptyset$). If no menu is a sock, then any item belonging to the set of menus definitely does not belong to the set of socks. Therefore, assuming the set of menus is not empty (which is standard in these problems), it is true that some menus are not socks. This conclusion logically follows.
Evaluating Conclusion II: No sock is a crocodile
As derived earlier, combining statements 1 and 2 leads to the conclusion that "Some crocodiles are socks". Conclusion II states "No sock is a crocodile". These two statements directly contradict each other. If it's true that some crocodiles are socks, then it cannot be true that no sock is a crocodile. Therefore, Conclusion II does not logically follow.
Evaluating Conclusion III: Some adapters are houses
The terms 'adapters' and 'houses' appear in Conclusion III but are not mentioned in any of the provided statements. Logical conclusions must be based solely on the information given in the statements. Since 'adapters' and 'houses' are unrelated to 'crocodiles', 'tubes', 'socks', or 'menus' within the context of the statements, this conclusion cannot be logically derived. Therefore, Conclusion III does not logically follow.
Final Conclusion
Based on the step-by-step analysis:
- Conclusion I logically follows from the statements.
- Conclusion II does not follow because it contradicts information derived from the statements.
- Conclusion III does not follow because it introduces terms not present in the statements.
Hence, only Conclusion I is a valid deduction.
Similar Questions
Two statements are given, followed by two conclusions numbered I and II. 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 book is a novel.
All novels are diaries.
Conclusions:
I. All diaries can never be books.
II. Some books are diaries.
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 rhombuses are tangents.
All chords are tangents.
Conclusions:
I. Some rhombuses being chords is a possibility.
II. Some tangents are rhombuses.
Three statements are followed by three conclusions numbered I, II, III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follows from the given statements.
Statements :
No Mango is a banana.
No banana is a guava.
Some guavas are oranges.
Conclusions :
(I) Some mangoes are oranges.
(II) Some guavas are mangoes.
(III) No orange is a banana.
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 tigers are fishes.
No elephant is a tiger.
Some deer are tigers.
Conclusions:
I. Some fishes are deer.
II. No elephant is a deer.
III. No deer is a fish.
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.
Statement :
All Bananas are Grapes.
All Papayas are Pineapple.
Some Pineapples are Banana.
Conclusions:
(I) Some Papayas are Grapes.
(II) Some Grapes are Pineapples.
(III) Some Bananas are Papayas.
Two statements are given, followed by two conclusions numbered I and II. 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:
Some defects are problems.
Some problems are solutions.
Conclusions:
I. Some defects being solutions is a possibility.
II. No solution is a defect.
Given below are two statements and two conclusions. Take the statements to be true even if they are at variance with commonly known facts, and decide whether the conclusion(s) follow(s) the given statements.
Statements:
Some bags are sacks.
Some sacks are juts.
Conclusions:
I. Some bags are juts.
II. Some juts are sacks.
Two statements are given, followed by two conclusions numbered I and II. Taking the statements to be true, even if they seem to be at variance from commonly known facts, decide which of the conclusions logically follows from the statements.
Statements:
All cycles are buses.
Some buses are trains.
Conclusions:
I. No cycle is train.
II. All cycles are trains.
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.
Statement:
Some figs are orange.
All oranges are grapes.
All mangoes are oranges.
Conclusions:
(I) Some figs are grapes.
(II) All mangoes are grapes.
(III) Some mangoes are figs.
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.
Statement :
All shoes are slippers.
All slippers are socks.
All socks are sandals
Conclusions:
(I) Some sandals are slippers
(II) Some socks are shoes.
(III) All sandals are shoes.
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.
