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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 conclusion(s) logically follow(s) from the statements. Statements: Some pens are red. All red are blue. Conclusion 1: All pens are blue. Conclusion 2: Some pens are not red.
Only conclusion 1 follows
Both conclusion 1 and 2 follow
Only conclusion 2 follows
Neither conclusion 1 nor 2 follows
Neither conclusion 1 nor 2 follows
In Syllogism, if a conclusion is not true in all possible Venn diagram scenarios, it is considered logically false.
In Syllogism, if a conclusion is not true in all possible Venn diagram scenarios, it is considered logically false.
Analyze the Statements
Draw two circles: one for Pens and one for Red, overlapping each other. Then, draw a larger circle for Blue that completely encloses the Red circle.
Evaluate Conclusion 1
Conclusion 1 (All pens are blue) is false because the intersection of Pens and Blue is not exhaustive; some pens might fall outside the Blue circle.
Evaluate Conclusion 2
Conclusion 2 (Some pens are not red) is false because, while possible, it is not definitely true; all pens could potentially be red in a specific scenario, violating the rule of absolute certainty.
A: Conclusion 1 is not necessarily true as some pens may lie outside the blue region. B: Both are false as neither is universally certain. C: Conclusion 2 is not necessarily true because the statements do not rule out that all pens could be red.
D is correct because neither conclusion logically follows from the given premises based on the possibility of different Venn diagram configurations.
Remember that in syllogisms, 'Some A are B' does not automatically mean 'Some A are not B' unless explicitly stated or proven by the negative constraint.
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