Question : Directions: Three statements are given followed by three conclusions numbered I, II and III. 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:
Some telescopes are periscopes.
Some telescopes are microscopes.
Some telescopes are kaleidoscopes.
Conclusions:
I. Some kaleidoscopes are telescopes.
II. Some microscopes are kaleidoscopes.
III. Some microscopes are telescopes.
Option 1: Only conclusion III follows
Option 2: Only conclusions I and III follow
Option 3: Only conclusions II and III follow
Option 4: All the conclusions follow
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Correct Answer: Only conclusions I and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some kaleidoscopes are telescopes – From the Venn diagram, it is evident that the circles representing kaleidoscopes and telescopes overlap and have some parts of their area in common. So, it can be concluded that some kaleidoscopes are telescopes. Thus, this conclusion follows.
Conclusion (II):
Some microscopes are kaleidoscopes – From the Venn diagram, it is evident that there is no direct relation between microscopes and kaleidoscopes. So, no definite relation can be drawn. Thus, this conclusion does not follow.
Conclusion (III):
Some microscopes are telescopes – From the Venn diagram, it is evident that the circles representing microscopes and telescopes overlap and have some parts of their area in common. So, it can be concluded that some microscopes are telescopes. Thus, this conclusion follows.
So, conclusions I and III follow. Hence, the second option is correct.
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