Question : Directions: In this question, 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 follows/follow from the statements.
Statements:
Some mirrors are glass.
All glasses are taps.
Some taps are pens.
Conclusions:
I. Some glass are mirrors.
II. All taps are glass.
III. Some pens are taps.
Option 1: None of the conclusions follows
Option 2: Only conclusions I and II follow
Option 3: Only conclusion II follows
Option 4: Only conclusions I and III follow
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Correct Answer: Only conclusions I and III follow
Solution : The possible Venn diagram according to the given statements –
Let's analyse the conclusions –
Conclusion I:
Some glass are mirrors – From the above Venn diagram, it is evident that the circles representing glass and mirror overlap each other and have a part of their areas in common. So, this conclusion follows.
Conclusion II:
All taps are glass – From the Venn diagram, it is evident that some part of the circle that represents taps is outside the circle that represents glass. So, from this, it can be concluded that some taps are glass. Thus, this conclusion does not follow.
Conclusion III:
Some pens are taps – From the above Venn diagram, it is evident that the circles representing pens and taps overlap each other and have a part of their areas in common. So, this conclusion follows.
So, only conclusions I and III follow . Hence, the fourth option is correct.
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