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 conclusions logically follow the given statements.
Statements:
I. All K are M.
II. Some K is Z.
Conclusions:
I. All M are Z.
II. All M are K.
III. Some M is K.
Option 1: All conclusion follows
Option 2: Neither conclusion follows
Option 3: Only conclusion III follows
Option 4: Both conclusions I and III follow
Correct Answer: Only conclusion III follows
Solution : The possible Venn diagram according to the given statement is as follows –
Let's analyse the conclusions –
Conclusion I:
All M are Z – From the Venn diagram, it is evident that the circles representing M and Z overlap and have some parts of their area in common. Thus, this conclusion does not follow.
Conclusion II:
All M are K – From the Venn diagram, it is evident that some parts of the circle representing M lie inside the circle representing K while some lie outside. Thus, this conclusion does not follow.
Conclusion III:
Some M is K – From the Venn diagram, it is evident that some parts of the circle representing M lie inside the circle representing K while some lie outside. Thus, it can be concluded that some M are K.
So, the only conclusion III follows. Hence, the
third option
is correct.
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