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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


Team Careers360 13th Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

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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