Statements:
All water is milk.
No milk is oil.
Conclusions:
(I) Some milk is water.
(II) No oil is water.
Logical Reasoning: Statement & Conclusion Analysis
This question tests our ability to apply logical deduction based on given statements. We need to determine if the provided conclusions necessarily follow from the premises, even if the premises seem unusual.
Statement Breakdown
Here are the statements we are given:
- Statement 1: All water is milk.
- Statement 2: No milk is oil.
Let's represent these using sets:
- Let \(W\) be the set of all water.
- Let \(M\) be the set of all milk.
- Let \(O\) be the set of all oil.
Statement 1 translates to: \(W \subseteq M\) (The set of water is a subset of the set of milk).
Statement 2 translates to: \(M \cap O = \emptyset\) (The intersection of the set of milk and the set of oil is empty; they are disjoint).
Conclusion (I): Analyzing 'Some milk is water'
The first conclusion is: Some milk is water.
From Statement 1, we know that All water is milk (\(W \subseteq M\)). This implies that any element that belongs to the set \(W\) must also belong to the set \(M\). In standard logical interpretations, we assume the categories mentioned (like 'water') are not empty. If there exists water, and all water is milk, then there must be at least some members in the set \(M\) that are also in the set \(W\).
Therefore, the statement "Some milk is water" logically follows. This is because the set \(W\) is contained within \(M\), meaning \(M\) contains all of \(W\). So, \(M \cap W = W\). Since we assume \(W\) is not empty, \(M \cap W \neq \emptyset\).
Conclusion (II): Analyzing 'No oil is water'
The second conclusion is: No oil is water.
We need to see if this follows from:
- Statement 1: \(W \subseteq M\)
- Statement 2: \(M \cap O = \emptyset\)
We know that the entire set of 'water' (\(W\)) is contained within the set of 'milk' (\(M\)). We also know that the set of 'milk' (\(M\)) and the set of 'oil' (\(O\)) are completely separate; they have no elements in common.
Since \(W\) is entirely inside \(M\), and \(M\) is entirely outside \(O\), it must be true that \(W\) is also entirely outside \(O\). There can be no overlap between the set of water and the set of oil.
In set notation: If \(W \subseteq M\) and \(M \cap O = \emptyset\), then it must be true that \(W \cap O = \emptyset\). This means "No oil is water".
Therefore, Conclusion (II) also logically follows from the given statements.
Final Deduction
Both Conclusion (I) and Conclusion (II) are logically derived from the provided statements.
Conclusion (I) follows from "All water is milk".
Conclusion (II) follows from combining "All water is milk" and "No milk is oil".
Thus, both conclusions 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:
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.- 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:
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.- 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 conclusion(s) logically follow(s) from the statements.
Statements:
Some woods are chisels.
Some chisels are graphs.
Conclusions:
(I) Some woods are graphs.
(II) All graphs are chisels.
