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 P are M.
II. No P is R.
Conclusion:
I. Some R are not P.
II. Some M are not R.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: Neither conclusion follows
Option 4: Both conclusions I and II follows
Correct Answer: Both conclusions I and II follows
Solution : According to the given statements, the venn diagram is given below –
Let's analyse the conclusions –
Conclusion (I):
Some R are not P – From the Venn diagram, it is evident that No P is R or No R is P. Thus if all R is not P is true it is obvious that some R is not P is also true. So, this conclusion follows.
Conclusion (II):
Some M are not R – From the Venn diagram, it is evident that all P are M and No P is R and all P is the part of M. So, some M are not R is true thus this conclusion follows.
So, both conclusions I and II follow. Hence, the fourth option is correct.
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