Question : Directions: Three statements are given, followed by three conclusions numbered I, II, and III. 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 classrooms are schools.
No school is a park.
All houses are parks.
Conclusions:
I. No house is a classroom.
II. No park is a classroom.
III. No school is a house.
Option 1: All of the conclusions follow
Option 2: Only conclusion II follows
Option 3: Only conclusion I follows
Option 4: Only conclusion III follows
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Correct Answer: All of the conclusions follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
No house is a classroom – Because there is a negative relation between school and park and the classroom is completely inside the school and the house is completely inside the park. Therefore, no house is a classroom is also true.
Conclusion (II):
No park is a classroom – Because there is a negative relation between school and park and the classroom is completely inside the school. Therefore, no park is a classroom is also true.
Conclusion (III):
No school is a house – Because there is a negative relation between school and the park and the house is completely inside the park. Therefore, no school is a house is also true.
So, all of the conclusions follow. Hence, the first option is correct.
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