Which of the following conclusion/s is/are valid based on the statements given below ?
Statement I : Some flowers are green.
Statement II : All green things are fruits.
Conclusion 1 : All fruits are flowers.
Conclusion 2 : All flowers are fruits.
Neither 1 nor 2
In a syllogism we accept the given statements as true, even if they seem unusual, and check whether each conclusion follows necessarily. A particular statement like Some X are Y combined with a universal statement All Y are Z gives only the particular result Some X are Z. A universal conclusion cannot be drawn from a premise that is only particular, and the distribution of terms must be respected.
Statement I: Some flowers are green.
Statement II: All green things are fruits.
Combining: Some flowers are green and all green things are fruits, so some flowers are fruits.
Conclusion 1: All fruits are flowers. The premises say nothing about every fruit; fruits may exist that are not flowers, so this does not follow.
Conclusion 2: All flowers are fruits. Only some flowers are known to be green, and only those are certainly fruits; the remaining flowers may or may not be fruits, so this does not follow either.
A Venn diagram confirms this: draw green inside fruits and let flowers overlap green. The flowers circle can extend outside fruits, and the fruits circle can extend outside flowers. Since neither universal statement is forced by the diagram, neither 1 alone, nor 2 alone, nor both can be accepted. The only valid inference, some flowers are fruits, is not among the given conclusions.
Hence, Neither 1 nor 2.
Similar Questions
Which of the following conclusion/s is/are valid based on the statements given below ?
Statement I : Some tigers are goats.
Statement II : All political leaders are intelligent.
Conclusion 1 : Some goats are not tigers.
Conclusion 2 : Some political leaders are intelligent.
Code :
Which of the following conclusion/s is/are valid based on the statements given below ?
Statement I : All tax payers are honest.
Statement II : All students are honest.
Conclusion 1 : Some tax payers are not honest.
Conclusion 2 : Some students are tax payers.
Code :
Which of the following is the valid conclusion based on the statements given below ?
Statement I : Some animals are intelligent.
Statement II : Intelligent animals are monkeys.
Conclusion 1 : All monkeys are intelligent.
Conclusion 2 : Horses are intelligent.
Code :
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.
