Statements:
Some woods are chisels.
Some chisels are graphs.
Conclusions:
(I) Some woods are graphs.
(II) All graphs are chisels.
Logical Reasoning Analysis
This question tests the ability to understand logical implications based on given statements. We need to determine if the provided conclusions necessarily follow from the statements.
Analyzing the Statements
Let's break down the given information:
- Statement 1: Some woods are chisels.
- Statement 2: Some chisels are graphs.
We are also given two potential conclusions:
- Conclusion (I): Some woods are graphs.
- Conclusion (II): All graphs are chisels.
The key is to see if these conclusions are *guaranteed* to be true based *only* on the statements.
Evaluating Conclusion (I): Some woods are graphs
Statement 1 tells us there is an overlap between the set of 'woods' and the set of 'chisels'. Statement 2 tells us there is an overlap between the set of 'chisels' and the set of 'graphs'.
However, the 'chisels' that are 'woods' might be completely different from the 'chisels' that are 'graphs'. The statements do not provide any information linking 'woods' directly to 'graphs'.
Consider this possibility:
- Group A: Woods that are chisels.
- Group B: Chisels that are graphs.
It's possible that Group A and Group B are distinct sets of chisels. Therefore, we cannot be certain that any woods are graphs.
Conclusion (I) does not necessarily follow.
Evaluating Conclusion (II): All graphs are chisels
Statement 2 says "Some chisels are graphs". This means there exists at least one thing that is both a chisel and a graph.
This statement does NOT mean that every single graph must also be a chisel. It's possible for there to be graphs that are not chisels. The statement only guarantees a partial overlap, not complete inclusion.
For example, imagine there are 10 graphs in total. Statement 2 only tells us that maybe 2 or 3 of those graphs are also chisels. It doesn't say anything about the other 7 or 8 graphs.
Conclusion (II) does not necessarily follow.
Final Determination
Since neither Conclusion (I) nor Conclusion (II) can be definitively proven true based solely on the given statements, we conclude that neither follows.
The correct logical outcome is that there is insufficient information to support either conclusion.
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.
