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.
Neither 1 or 2 follows
Analysing the Statements on Rivers and Gods
The question asks us to consider two statements as true and determine which conclusions logically follow from them. These types of questions test our ability to perform logical deduction based on given premises.
The statements are:
- Statement 1: All rivers are holy.
- Statement 2: All gods are holy.
We need to analyze these statements to understand the relationship between 'rivers', 'gods', and 'holy' things. We can think of these as categories or sets.
- Statement 1 tells us that the set of 'rivers' is completely contained within the set of 'holy' things.
- Statement 2 tells us that the set of 'gods' is also completely contained within the set of 'holy' things.
Both rivers and gods are subsets of holy things. However, the statements do not provide any direct information about the relationship between rivers and gods themselves. They could be the same set, entirely separate sets within 'holy' things, or overlapping sets.
Evaluating the Conclusions Based on the Statements
Let's examine each conclusion provided:
- Conclusion 1: All rivers are gods.
- Conclusion 2: All gods are rivers.
Analysing Conclusion 1: All rivers are gods.
This conclusion claims that the set of 'rivers' is completely contained within the set of 'gods'. Do our statements support this?
We know all rivers are holy, and all gods are holy. Consider a scenario where there are holy things which are neither rivers nor gods, or where rivers and gods are distinct groups within the holy things. For example:
- Suppose 'Holy' includes rivers, gods, and sacred texts.
- Statement 1: All rivers are holy (True).
- Statement 2: All gods are holy (True).
- In this scenario, rivers and gods could be completely separate groups. Are all rivers necessarily gods? No. A river is holy, but that doesn't automatically make it a god.
Since we can have a situation where the statements are true, but Conclusion 1 is false, Conclusion 1 cannot be definitely drawn from the statements.
Analysing Conclusion 2: All gods are rivers.
This conclusion claims that the set of 'gods' is completely contained within the set of 'rivers'. Do our statements support this?
Again, we know all rivers are holy, and all gods are holy. Using the same reasoning as above, the statements place both rivers and gods within the larger set of holy things, but do not define their relationship to each other. For example:
- Suppose 'Holy' includes rivers and gods, and nothing else.
- Statement 1: All rivers are holy (True).
- Statement 2: All gods are holy (True).
- Even in this simplified case, the sets of rivers and gods could still be distinct. Are all gods necessarily rivers? No. A god is holy, but that doesn't automatically make it a river.
Since we can have a situation where the statements are true, but Conclusion 2 is false, Conclusion 2 cannot be definitely drawn from the statements.
Summary of Conclusions from Logic Statements
Based on the analysis, neither conclusion 1 nor conclusion 2 necessarily follows from the given statements. The statements establish that both 'rivers' and 'gods' are subsets of 'holy' things, but they provide no information about the intersection or containment relationship between 'rivers' and 'gods'.
Therefore, neither of the given conclusions can be definitely drawn from the given statements.
| Statement/Conclusion | Relationship | Follows? |
|---|---|---|
| Statement 1: All rivers are holy. | Rivers $\subseteq$ Holy | Given as True |
| Statement 2: All gods are holy. | Gods $\subseteq$ Holy | Given as True |
| Conclusion 1: All rivers are gods. | Rivers $\subseteq$ Gods | No (Not necessarily true based on statements) |
| Conclusion 2: All gods are rivers. | Gods $\subseteq$ Rivers | No (Not necessarily true based on statements) |
Based on this logical analysis, the correct determination is that neither conclusion 1 nor conclusion 2 follows.
Revision Table for Logic Reasoning
| Concept | Description | Relevance to Problem |
|---|---|---|
| Statements (Premises) | Assumed to be true, form the basis for deduction. | "All rivers are holy," "All gods are holy." |
| Conclusion | A statement that is claimed to logically follow from the premises. | "All rivers are gods," "All gods are rivers." |
| Logical Deduction | The process of reasoning from one or more general statements (premises) to reach a logically certain conclusion. | We used deduction to see if conclusions follow from statements. |
| Categorical Syllogism | A type of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. | This question is a simple form involving three categories (rivers, gods, holy). |
| Validity | An argument is valid if it is impossible for the premises to be true and the conclusion false. We checked for validity of the conclusions. | Neither conclusion was found to be validly drawn. |
Additional Information on Syllogism and Venn Diagrams
Problems like this can often be visualised using Venn diagrams. For the given statements:
- Draw a large circle representing 'Holy Things'.
- Draw a circle inside the 'Holy Things' circle representing 'Rivers'. Statement 1 says all rivers are holy, so the 'Rivers' circle is entirely within the 'Holy Things' circle.
- Draw another circle inside the 'Holy Things' circle representing 'Gods'. Statement 2 says all gods are holy, so the 'Gods' circle is entirely within the 'Holy Things' circle.
Now, look at the relationship between the 'Rivers' circle and the 'Gods' circle. Based on the statements alone, the 'Rivers' circle and the 'Gods' circle could:
- Completely overlap (Rivers = Gods).
- Be entirely separate (No rivers are gods, and no gods are rivers).
- Partially overlap (Some rivers are gods, and some gods are rivers).
Since the statements allow for multiple possibilities regarding the relationship between 'rivers' and 'gods', we cannot definitively conclude that "All rivers are gods" (Conclusion 1) or "All gods are rivers" (Conclusion 2). For a conclusion to definitely follow, it must be true in ALL possible scenarios where the statements are true.
This type of logic problem highlights that correlation (both being holy) does not imply causation or a direct relationship between the two correlating entities (rivers and gods).
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. 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.
