Question : Directions: Two 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:
All bags are pens
All pencils are pens
Conclusions:
I. Some pens are bags
II. All bags are pencils
III. Some pens are pencils
Option 1: Both conclusions II and III follow
Option 2: Conclusions I, II and III follow
Option 3: Both conclusions I and II follow
Option 4: Both conclusions I and III follow
Correct Answer: Both conclusions I and III follow
Solution : Given:
According to the given statements, the possible Venn diagram is as follows –
Let's analyse the conclusions –
Conclusion I:
Some pens are bags – From the Venn diagram, it is evident that the circle representing bags is completely overlapped by the circle representing pens. Thus, it can be concluded that some pens are bags.
Conclusion II:
All bags are pencils – From statements I and II, it can be deduced that both bags and pencils are pens. However, no relation between bags and pencils is mentioned. Thus, this conclusion does not follow.
Conclusion III:
Some pens are pencils – From the Venn diagram, it is evident that the circle representing pencils is completely overlapped by the circle representing pens. So, it can be concluded that some pens are pencils.
So, both conclusions I and III follow. Hence, the fourth option is correct.
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