In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
Some raisins are grapes.
All grapes are apples.
All raisins are fruits.
Conclusions:
I. Some fruits are apples.
II. Some apples are raisins.
Statement Conclusion Logic Problems
This problem involves analyzing logical statements and conclusions to determine their validity. We need to check if the given conclusions can be logically derived from the provided statements.
Analyzing Given Statements
- Statement 1: Some raisins are grapes. (This indicates a partial overlap between the set of raisins and the set of grapes.)
- Statement 2: All grapes are apples. (This means the entire set of grapes is contained within the set of apples.)
- Statement 3: All raisins are fruits. (This means the entire set of raisins is contained within the set of fruits.)
Intermediate Conclusion Derivation
Let's combine the first two statements:
- From Statement 1, we know there exists at least one raisin that is also a grape.
- From Statement 2, we know that every grape is an apple.
- Therefore, if there's a raisin that is a grape, and all grapes are apples, then that specific raisin must also be an apple.
- This allows us to derive an intermediate conclusion: Some raisins are apples.
Conclusion I: Some fruits are apples
Now, let's evaluate Conclusion I using the statements and our derived conclusion:
- We know from Statement 3: All raisins are fruits.
- We derived: Some raisins are apples.
- Since all the raisins mentioned in "All raisins are fruits" are indeed fruits, and we know some of these raisins are also apples, it logically follows that those specific raisins represent fruits that are also apples.
- Therefore, Some fruits are apples. Conclusion I logically follows.
Conclusion II: Some apples are raisins
Let's evaluate Conclusion II:
- We derived the statement: Some raisins are apples.
- This statement means that there is at least one member that belongs to both the 'raisins' category and the 'apples' category.
- The statement "Some A are B" is logically equivalent to "Some B are A".
- Thus, "Some raisins are apples" logically implies Some apples are raisins. Conclusion II logically follows.
Overall Validity
Based on the step-by-step analysis:
- Conclusion I is valid.
- Conclusion II is valid.
Both conclusions logically follow from the given statements.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
