In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements. Statements: I. No tyre are white. II. All grey are white. Conclusions: I. No white is tyre. II. No tyre is grey. III. Some white are not grey.
Both conclusions I and II follows
Logical Deduction: Tyre, White, and Grey Objects
This question tests our ability to understand logical implications between statements and conclusions. We are given two statements and asked to identify which conclusions necessarily follow from them, even if the statements contradict common knowledge.
Statements Provided
- Statement I: No tyre are white.
- Statement II: All grey are white.
Conclusions to Evaluate
- Conclusion I: No white is tyre.
- Conclusion II: No tyre is grey.
- Conclusion III: Some white are not grey.
Analyzing Statement I: No tyre are white
This statement establishes a complete separation between the category 'tyre' and the category 'white'. It means there is no overlap between these two sets. In formal logic, if we represent 'tyre' as T and 'white' as W, this statement is: No T is W.
Analyzing Statement II: All grey are white
This statement indicates that the entire category 'grey' is included within the category 'white'. Every single grey item is also a white item. Using notation, if 'grey' is G, this statement is: All G are W. This implies that the set G is a subset of the set W ($G \subseteq W$).
Evaluating Conclusion I: No white is tyre
Statement I says No T is W. This relationship is symmetrical. If no tyre is white, it directly means that no white thing can be a tyre. Think of it like sets: if set T and set W do not intersect, then W and T also do not intersect. Therefore, No W is T is a valid conclusion.
Result: Conclusion I logically follows.
Evaluating Conclusion II: No tyre is grey
We know from Statement I that No T is W (Tyre and White are separate sets).
We know from Statement II that All G are W (The Grey set is entirely inside the White set).
Since the entire Grey set is inside the White set, and the Tyre set is completely outside the White set, the Tyre set must also be completely outside the Grey set. If something cannot be white, it definitely cannot be grey, because every grey thing is white.
Result: Conclusion II logically follows.
Evaluating Conclusion III: Some white are not grey
Statement II tells us All G are W. This means the set of grey things is contained within the set of white things ($G \subseteq W$).
Conclusion III says "Some white are not grey". This means there must be at least one white thing that is not grey ($ \exists x (x \in W \land x \notin G) $).
However, Statement II only guarantees that all grey things are white. It does not prevent the possibility that *all* white things are also grey. If the set of 'white' things and the set of 'grey' things were exactly the same, then Statement II would still be true, but Conclusion III ("Some white are not grey") would be false.
Because this conclusion is not guaranteed to be true under all conditions allowed by the statements, it does not logically follow.
Result: Conclusion III does not necessarily follow.
Summary of Logical Following
Based on our analysis:
- Conclusion I: Follows
- Conclusion II: Follows
- Conclusion III: Does not follow
Therefore, the only conclusions that logically follow from the given statements are Conclusion I and Conclusion II.
Similar Questions
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.
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:
Some spices are medicines.
All medicines are chemicals.
No chemical is cheap.
Conclusions:
I. Some medicines are cheap.
II. Some chemicals are spices.
III. No medicine is cheap.
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 oranges are apples.
Some oranges are bananas.
All bananas are fruits.
Conclusions:
I. Some fruits are apples.
II. Some apples are bananas.
III. Some oranges are fruits.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some Z are X.
II. Some W are Z.
Conclusions:
I. Some X are not W.
II. Some X are not Z.
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:
Some mobiles are flat.
All flats are TVs.
Some TVs are plastic.
Conclusions:
I. Some mobiles are TVs.
II. Some flats are plastic.
III. All plastic are TVs.
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:
No cup is a plate.
All cups are utensils.
Some bottles are cups.
Conclusions:
I. Some utensils are not plates.
II. Some bottles are not plates.
III. No bottle is a plate.
Three statements are followed by three conclusions numbered I, II and 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 follow/s from the given statements.
Statements:
Some watches are projectors.
All projectors are lamps.
Some heaters are watches.
Conclusions:
(I) Some heaters are projectors.
(II) Some lamps are heaters.
(III) All watches are lamps
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. No A is B.
II. No C is B.
Conclusion:
I. Some C are not A.
II. Some A are B.
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 benches are tables.
Some tables are chairs.
Some chairs are pencils.
Conclusions:
I. Some benches are chairs.
II. Some tables are pencils.
III. Some pencils are chairs.
IV. Some pencils are tables.
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.
