Statement: Some ponds are lakes. Some lakes are rivers. Some rivers are seas
Conclusions:
1. Some seas are lakes
2. No sea is a lake
Statements Analysis
We are given three statements:
- Some ponds are lakes.
- Some lakes are rivers.
- Some rivers are seas.
We need to determine which of the following conclusions logically follows:
- Some seas are lakes.
- No sea is a lake.
Logical Deduction
Let P represent the set of Ponds, L the set of Lakes, R the set of Rivers, and S the set of Seas.
The given statements can be represented as:
- $P ∩ L ≠ ∅$ (Some ponds are lakes)
- $L ∩ R ≠ ∅$ (Some lakes are rivers)
- $R ∩ S ≠ ∅$ (Some rivers are seas)
We need to find the logical relationship between Lakes (L) and Seas (S) based on these premises.
The premises establish that the set of Lakes (L) has a non-empty intersection with the set of Rivers (R), and the set of Rivers (R) also has a non-empty intersection with the set of Seas (S).
Conclusion Evaluation
The crucial point is that the overlap between Lakes and Rivers ($L ∩ R$) might involve different members of the River set than the overlap between Rivers and Seas ($R ∩ S$).
- Scenario 1: It is possible that the rivers which are lakes are completely different from the rivers which are seas. In this case, there might be no overlap between lakes and seas ($L ∩ S = ∅$). This would make Conclusion 2 (No sea is a lake) true.
- Scenario 2: It is also possible that the rivers which are lakes could overlap with the rivers which are seas. In this scenario, there would be an overlap between lakes and seas ($L ∩ S ≠ ∅$). This would make Conclusion 1 (Some seas are lakes) true.
Since the given statements allow for both possibilities (overlap or no overlap between Lakes and Seas), neither Conclusion 1 nor Conclusion 2 is guaranteed to be true in all cases.
However, the relationship between Lakes and Seas must be one of the two possibilities: either they overlap (Conclusion 1 is true) or they do not overlap (Conclusion 2 is true). The premises do not allow for any other relationship (like 'All seas are lakes' or 'All lakes are seas'). Because the premises allow for scenarios validating Conclusion 1, and also for scenarios validating Conclusion 2, the correct choice is that either one or the other follows.
Similar Questions
- Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
All water is milk.
No milk is oil.
Conclusions:
(I) Some milk is water.
(II) No oil is water. - Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some vegetables are fruits.
Some fruits are sweets.
Conclusions:
(I) Some fruits are vegetables.
(II) Some sweets are vegetables. - Two statements are given, followed by two conclusions, I and II. Consider the statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions, if any, follow (s) from the given statements.
Statement 1: All bees are hornets.
Statement 2: Some bees are wasps.
Conclusion I: Some hornets are wasps.
Conclusion II: Some wasps are bees. - Two statements are given, followed by three conclusions, I, II and III. Consider the statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions, if any, follow (s) from the given statements.
Statement 1: No boats are ships.
Statement 2: All ship are steamers.
Conclusion I: Some boats are steamers.
Conclusion II: No ships are boats.
Conclusion III: Some steamers are ships. - Given below are two statements, followed by three conclusions, I, II and III. You have to consider the statements to be true even if they seems to be at variance with commonly known facts. You have to decide which of the given conclusions, if any, follow(s) from the given statements.
Statement 1 : All polymers are plastic.
Statement 2 : No rubber is plastic.
Conclusion I : Some polymers are rubber.
Conclusion II : Some plastics are polymer.
Conclusion III : No polymer is rubber. - Given below are two statements, followed by two conclusions, I and II. You have to consider the statements to be true even if they seems to be at variance with commonly known facts. You have to decide which of the given conclusions, if any, follow(s) from the given statements.
Statement 1 : All minutes are seconds.
Statement 2 : No seconds are hours.
Conclusion I : No hours are seconds.
Conclusion II : Some minutes are hours. - Two statements are given, followed by three conclusions, I, II and III. Consider the statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions, if any, follow (s) from the given statements.
Statement 1: No boats are ships.
Statement 2: All ship are steamers.
Conclusion I: Some boats are steamers.
Conclusion II: No ships are boats.
Conclusion III: Some steamers are ships. - Two statements are given, followed by two conclusions, I and II. Consider the statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions, if any, follow (s) from the given statements.
Statement 1: All bees are hornets.
Statement 2: Some bees are wasps.
Conclusion I: Some hornets are wasps.
Conclusion II: Some wasps are bees. Consider the given statement as true and decide which of the given conclusions can definitely be drawn from the given statements:
Statement:
All rivers are holy. All gods are holy.
Conclusion:
1. All rivers are gods.
2. All gods are rivers.
In this question, two statements are given, followed by three conclusions labelled I, II and III. You have to consider the statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions, if any, follow(s) from the given statements.
Statements:
All mansions are palaces.
No castles are palaces.
Conclusions:
I: Some palaces are mansions.
II: Some castles are mansions.
II: No mansions are castles.
Important Questions from Syllogism
- Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
All water is milk.
No milk is oil.
Conclusions:
(I) Some milk is water.
(II) No oil is water. - Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some vegetables are fruits.
Some fruits are sweets.
Conclusions:
(I) Some fruits are vegetables.
(II) Some sweets are vegetables. - 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 sparrows are owls.
No sparrow is a parrot.
Conclusions:
(I): No owl is a parrot.
(II): No parrot is a sparrow. 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 forests are hills.
Some hills are deserts.
Conclusions:
(I): All hills are forests.
(II): Some deserts are hills.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 bottles are ludo.
All ludo are dancer.
Conclusions:
(I): Some dancers are ludo.
(II): All bottles are dancers.
