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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 girls are honest. Priya is honest. Conclusion 1: Priya is a girl. Conclusion 2: All honest people are girls.
Only conclusion (1) follows
Only conclusion (2) follows
None of the conclusions follow
Both conclusion (1) and conclusion (2) follow
None of the conclusions follow
In Syllogism, don't confuse the subset with the superset. Since all girls are honest, girls are a subset of honest people; thus, being honest doesn't prove one is a girl, nor does being a girl guarantee one is the only person who can be honest.
In Syllogism, don't confuse the subset with the superset. Since all girls are honest, girls are a subset of honest people; thus, being honest doesn't prove one is a girl, nor does being a girl guarantee one is the only person who can be honest.
Analyze Statement 1
All girls are honest implies a set relationship: the set of Girls is contained entirely within the set of Honest People. The reverse (All honest people are girls) is not necessarily true.
Analyze Statement 2 and Conclusions
Priya is honest only places her inside the larger circle (Honest People). She could be inside the smaller circle (Girls) or in the area of Honest People that is not Girls. Therefore, we cannot conclude she is a girl.
A: Incorrect because Priya could be an honest person who is not a girl. B: Incorrect because the statement says all girls are honest, not that honesty is exclusive to girls. D: Incorrect because both conclusions are logical fallacies based on the provided statements.
C is correct because neither conclusion is logically necessitated by the statements; Priya's honesty does not confirm her gender, and the statements do not limit honesty only to girls.
Beware of 'Affirming the Consequent'. If A implies B, it does not mean B implies A. Always draw the Venn diagram to see if the conclusion holds true in all possible scenarios.