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: Conclusions:
All forests are hills.
Some hills are deserts.
(I): All hills are forests.
(II): Some deserts are hills.
Analyzing Statements and Conclusions
This problem requires us to evaluate two conclusions based on two given statements. We need to determine which conclusion logically follows from the statements, assuming the statements are true.
Understanding the Statements
- Statement 1: All forests are hills.
- Statement 2: Some hills are deserts.
Evaluating the Conclusions
We can use logical deduction or Venn diagrams to analyze the conclusions.
Conclusion (I): All hills are forests.
- Statement 1 states that the category 'forests' is entirely contained within the category 'hills' (All F are H).
- This does not mean that the category 'hills' is entirely contained within 'forests'. It's possible for there to be hills that are not forests.
- Therefore, the conclusion "All hills are forests" (All H are F) does not necessarily follow from the statements.
Conclusion (II): Some deserts are hills.
- Statement 2 states "Some hills are deserts". This means there is at least one entity that is both a hill and a desert.
- The relationship "Some A are B" is logically equivalent to "Some B are A".
- So, if "Some hills are deserts" is true, then "Some deserts are hills" must also be true.
- Therefore, Conclusion II logically follows from the statements.
Final Deduction
Based on the analysis:
- Conclusion I is invalid.
- Conclusion II is valid.
Thus, only Conclusion II follows from the given statements.
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 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.
