Question : Directions: Three statements are given, followed by four conclusions numbered I, II, III, and IV. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: No blue is red. Some green are red. All yellow is green. Conclusions: I. Some yellow are red. II. No yellow is red. III. Some green are blue. IV. No green is blue.
Option 1: Only conclusions I and IV follow
Option 2: Only conclusions I and II follow
Option 3: Only conclusions III and IV follow
Option 4: None of the conclusions follow
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Correct Answer: None of the conclusions follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some yellow is red – From the Venn diagram, there is no definite relation between yellow and red. Therefore, this conclusion is false. Conclusion (II): No yellow is red – From the Venn diagram, there is no definite relation between yellow and red. Therefore, this conclusion is false. Conclusion (III): Some green are blue – From the Venn diagram, there is no definite relation between green and blue. Therefore, this conclusion is false. Conclusion (IV): No green is blue – From the Venn diagram, there is no definite relation between green and blue. Therefore, this conclusion is false.
So, none of the conclusions follow. Hence, the fourth option is correct.
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