Question : Directions: Consider the given statement(s) to be true and decide which of the given conclusions can be drawn from the given statements.
Statements:
All books are trees.
All trees are lions.
Conclusions:
I. All books are lions.
II. All lions are books.
III. All trees are books.
IV. Some lions are books.
Option 1: Only conclusions I and III follow
Option 2: Only conclusions I and IV follow
Option 3: None of the conclusions follows
Option 4: All conclusions follow
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Correct Answer: Only conclusions I and IV follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
All books are lions – From the Venn diagram, it is evident that the circle representing books completely lies inside the circle representing lions. So, from this, it can be concluded that all books are lions. Therefore, this conclusion follows.
Conclusion (II):
All lions are books – From the Venn diagram, it is evident that some parts of the circle representing lions lie outside the circle representing books while some lie inside. So, from this, it can be concluded that some lions are books. Therefore, this conclusion does not follow.
Conclusion (III):
All trees are books – From the Venn diagram, it is evident that some parts of the circle representing trees lie outside the circle representing books while some lie inside. So, from this, it can be concluded that some trees are books. Therefore, this conclusion does not follow.
Conclusion (IV):
Some lions are books – From the Venn diagram, it is evident that some parts of the circle representing lions lie outside the circle representing books while some lie inside. So, from this, it can be concluded that some lions are books. Therefore, this conclusion follows.
Therefore, only conclusions I and IV follow. Hence, the second option is correct.
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