Question : Directions: In the following question, two statements are given followed by two conclusions I and II. You have to consider the two statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow from the given statements. Statements: Some principals are teachers. All teachers are students. Conclusions: I. All principals are students. II. Some students are principals.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: Both conclusion I and conclusion II follow
Option 4: Neither conclusion I nor conclusion II follows
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Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All principals are students – From the Venn diagram, it is evident that the circles representing principals and students overlap each other and have a part of their area in common. So, from this, it can be concluded that some principals are students. Thus, this conclusion does not follow. Conclusion (II): Some students are principals – From the Venn diagram, it is evident that the circles representing principals and students overlap each other and have a part of their area in common. So, from this, it can be concluded that some students are principals. Thus, this conclusion follows.
So, only the conclusion II follows. Hence, the second option is correct.
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