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 boxes are cubes.
All cubes are squares.
Conclusions:
I. Some boxes are squares.
II. Some squares are not cubes.
Option 1: Only conclusion I follows
Option 2: Both conclusions I and II follow
Option 3: Neither conclusion I nor II follows
Option 4: Only conclusion II follows
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):
Some boxes are squares – From the Venn diagram, we can see that the circle representing boxes is completely overlapped by the circle representing squares. Since all boxes are squares. Therefore, some boxes will be squares. Thus, this conclusion follows.
Conclusion (II):
Some squares are not cubes – It is a possibility that the circle representing squares is not completely overlapped by the circle representing cubes. But this is not definite. Thus, this conclusion does not follow.
So, the only conclusion I follows. Hence, the first option is correct.
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