Question : Directions: In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows the given statements.
Statements:
I. Some red are black.
II. No white is black.
Conclusions:
I. No black is white.
II. No white is red.
III. No black is red.
Option 1: Neither conclusion follows
Option 2: All conclusions follow
Option 3: Only conclusion I follows
Option 4: Both conclusions II and III follows
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Correct Answer: Only conclusion I follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
No black is white
– From the Venn diagram, it is evident that there is a negative relation between black and white. So, it can be concluded that no black is white.
Conclusion (II):
No white is red
– From the Venn diagram, there is no definite relation between red and white. So, this conclusion does not follow.
Conclusion (III):
No black is red
– From the Venn diagram, it is evident that the circles representing black and red intersect and have a common area between them. So, this conclusion does not follow.
So, the only conclusion I follows. Hence, the third option is correct.
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