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 from the statements.
Statements:
I. All blocks are toys.
II. All toys are books.
III. All books are stories.
Conclusions:
I. Some toys are blocks.
II. Some blocks are books.
III. Some stories are toys.
Option 1: Only conclusions I and III follow
Option 2: Only conclusions II and III follow
Option 3: Only conclusions I and II follow
Option 4: All the conclusions follow
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Correct Answer: All the conclusions follow
Solution : The possible Venn diagram according to the statements will be –
Let's analyse the conclusions –
Conclusion (I):
Some toys are blocks – From the Venn diagram, it is clear that the circle that represents toys is overlapped by the circle that represents blocks and has some areas in common. So, some toys are blocks. Therefore, this conclusion follows.
Conclusion (II):
Some blocks are books – From the Venn diagram, it is clear that the circle that represents blocks lies inside the circle that represents books. So, all blocks are books and some blocks are books is also true. Therefore, this conclusion follows.
Conclusion (III):
Some stories are toys – From the Venn diagram, it is clear that the circle that represents toys is overlapped by the circle that represents stories and has some areas in common. So, some stories are toys. Therefore, this conclusion follows.
So, all the conclusions follow. Hence, the fourth option is correct.
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