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 :
Neither 1 nor 2
Both premises are universal affirmatives of the form "All A are B", and both share the same predicate — honest. So tax payers form a subset of the honest, and students form a subset of the honest, and nothing at all is stated about how those two subsets sit relative to each other.
Conclusion 1 is invalid. Statement I says every tax payer is honest. "Some tax payers are not honest" directly contradicts that statement, so far from following from the premises, it is ruled out by them.
Conclusion 2 is invalid. Two subsets of the same larger set need not meet. Picture the honest people as a circle containing two smaller circles, one of tax payers and one of students; those two smaller circles may overlap, but they may equally be drawn entirely apart. Since a case exists in which no student is a tax payer, the conclusion is not necessarily true, and a syllogistic conclusion must hold in every possible arrangement.
This also matches the formal rule that a middle term must be distributed at least once for a valid conclusion. Here the middle term "honest" is the predicate of both affirmative premises and so is undistributed in each, which blocks any conclusion linking tax payers with students.
Hence neither conclusion 1 nor conclusion 2 is valid.
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.
