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 boats are ships.
All ships are yachts.
All yachts are barges.
Conclusions:
I. Some barges are ships.
II. Some barges are boats.
III. Some yachts are boats.
Option 1: Only conclusions II and III follow
Option 2: Only conclusions I and III follow
Option 3: All conclusions follow
Option 4: Only conclusions I and II follow
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Correct Answer: All conclusions follow
Solution : According to the statements, the following Venn diagram can be drawn –
Let's analyse the conclusions –
Conclusion I:
Some barges are ships –
From the Venn diagram, it is evident that the circle that represents ships is overlapped by the circle that represents barges and has some areas in common. So, some barges are ships. Therefore, this conclusion follows
.
Conclusion II:
Some barges are boats – From the above diagram, it is evident that the circles representing barges and boats overlap each other and have a part of their areas in common. So, some barges are boats. Therefore, this conclusion follows.
Conclusion III:
Some yachts are boats – From the above diagram, it is evident that the circles representing yachts and boats overlap each other and have a part of their areas in common. So, some yachts are boats. Therefore, this conclusion follows.
So, all conclusions follow according to the statements. Hence, the third option is correct.
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