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:
Some windows are houses.
Some windows are roofs.
Conclusions:
I. Some roofs are houses.
II. Some roofs are windows.
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 II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some roofs are houses – From the Venn diagram, it is evident that there is no direct relation between roofs and houses. So, no definite relation can be drawn. Thus, this conclusion does not follow.
Conclusion (II):
Some roofs are windows – From the Venn diagram, it is evident that the two circles representing roofs and windows overlap and have a part of their area in common. So, it can be concluded that some roofs are windows. Thus, this conclusion follows.
So, the only conclusion II follows. Hence, the fourth option is correct.
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