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.
Analyzing Syllogism Statements
We need to determine which conclusions logically follow from the given statements.
Statement 1: All polymers are plastic.This means the set of 'polymers' is entirely contained within the set of 'plastic'.
Statement 2: No rubber is plastic.This means the set of 'rubber' and the set of 'plastic' are completely separate; they have no common elements.
Evaluating Conclusions
Let's analyze each conclusion based on the statements:
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Conclusion I: Some polymers are rubber.
Since all polymers are plastic (Statement 1) and no rubber is plastic (Statement 2), polymers and rubber cannot overlap. Therefore, this conclusion is false.
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Conclusion II: Some plastics are polymer.
Because all polymers are plastic (Statement 1), it logically follows that the set of plastic includes all polymers. Thus, some members of the 'plastic' set are indeed 'polymers'. This conclusion is true.
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Conclusion III: No polymer is rubber.
From Statement 1, polymers are a subset of plastics. From Statement 2, rubber is entirely separate from plastics. Therefore, polymers must also be entirely separate from rubber. This conclusion is true.
Determining Valid Conclusions
Based on the analysis:
- Conclusion I does not follow.
- Conclusion II follows.
- Conclusion III follows.
Therefore, only conclusions II and III are valid.
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 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.- Take the given statements to be true and decide which of the conclusions logically follows from the given statements.
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
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.
