Question : Directions: Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusions logically follow/s from the given statements.
Statements:
Some apples are oranges.
All oranges are bananas.
All bananas are mangoes.
Conclusions:
I. Some mangoes are oranges.
II. Some bananas are apples.
Option 1: Only conclusion I is true
Option 2: Both conclusions I and II are true
Option 3: Neither conclusion I nor II is true
Option 4: Only conclusion II is true
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Correct Answer: Both conclusions I and II are true
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some mangoes are oranges – From the Venn diagram, it is clear that some parts of the mango region lie outside the banana region and some overlap the region of the banana. Therefore, this conclusion follows.
Conclusion (II):
Some bananas are apples – From the Venn diagram, the circle of bananas and apples overlap and have some common area between them. Therefore, this conclusion follows.
So, both conclusions follow. Hence, the second option is correct.
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