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. All colours are small.
II. No small is big.
Conclusions:
I. All small are colour.
II. Some small are colour.
III. All the big are colour.
Option 1: Neither conclusion follows
Option 2: Only conclusion III follows
Option 3: Only conclusion II follows
Option 4: Both conclusions I and II follow
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Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion I:
All small are colour – From the Venn diagram, it is evident that some parts of the circle representing small lie outside the circle representing colours while some lie inside. So, it can be concluded that some small are colours, not all.
Conclusion II:
Some small are colour – From the Venn diagram, it is evident that some parts of the circle representing small lie outside the circle representing colours while some lie inside. So, it can be concluded that some small are colours.
Conclusion III:
All big are colour – In the Venn diagram, there is no definite relation between the circles that represent big and colour. Therefore, this conclusion does not follow.
Therefore, the only conclusion II follows. Hence, the third option is correct.
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