Question : Directions: Two statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All bags are black.
Some bags are white.
Conclusions:
I. Some black are white.
II. All black are bags.
Option 1: Neither conclusion I nor II follows
Option 2: Only conclusion I follows
Option 3: Both conclusions I and II follow
Option 4: Only conclusion II follows
Correct Answer: Only conclusion I follows
Solution : The possible Venn diagram according to the given statement is as follows –
Let's analyse the conclusions –
Conclusion I:
Some blacks are white – From the Venn diagram, it is evident that the circles representing black and white overlap and have a part of their area in common. So, it can be concluded that some blacks are white. Thus, this conclusion follows.
Conclusion II:
All blacks are bags – From the Venn diagram, it is evident that some parts of the circle representing blacks lie inside the circle representing bags while some lie outside. So, from this, it can be concluded that some blacks are white. Thus, this conclusion does not follow.
So, the only conclusion I follows. Hence, the second option is correct.
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