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 bikes are cycles.
II. Some cycles are tub.
Conclusions:
I. All tubs are bikes.
II. All cycles are tub.
III. All cycles are bikes.
Option 1: All conclusion follows
Option 2: Only conclusion II follows
Option 3: Neither conclusion follows
Option 4: Both conclusions I and II follow
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Correct Answer: Neither conclusion follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
All tubs are bikes – From the Venn diagram, we can see that there is no definite relation between tubs and bikes. So, this conclusion does not follow.
Conclusion (II):
All cycles are tubs – From the Venn diagram, we can see that the two circles representing cycles and tubs overlap and have a part of their area in common. So, this conclusion does not follow.
Conclusion (III):
All cycles are bikes – From the Venn diagram, it is evident that some parts of the circle representing cycles lie inside the circle representing bikes while some lie outside. So, this conclusion does not follow.
So, none of the conclusions follows. Hence, the third option is correct.
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