Question : Directions: Three statements are followed by three conclusions numbered I, II, and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow/s from the given statements.
Statements:
Some watches are projectors.
All projectors are lamps.
Some heaters are watches.
Conclusions:
(I) Some heaters are projectors.
(II) Some lamps are heaters.
(III) All watches are lamps.
Option 1: Only conclusion II follows
Option 2: None of the conclusions follow
Option 3: Only conclusion I follows
Option 4: Either conclusion I or conclusion III follows
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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 heaters are projectors – From the Venn diagram, it is evident that there is no direct relation between heaters and projectors. So, no definite relation can be drawn. Therefore, this conclusion does not follow.
Conclusion (II):
Some lamps are heaters – From the Venn diagram, it is evident that there is no direct relation between lamps and heaters. So, no definite relation can be drawn. Therefore, this conclusion does not follow.
Conclusion (III):
All watches are lamps – From the Venn diagram, it is evident that the circles representing watches and lamps overlap each other and have some parts of their area in common. So, from this, it can be concluded that some watches are lamps. Therefore, this conclusion does not follow.
So, none of the conclusions follow. Hence, the second option is correct.
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