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 males are boys.
Some teachers are boys.
All students are teachers.
Conclusions:
I. Some boys are males.
II. Some teachers are students.
III. All males are students.
Option 1: All conclusions follow
Option 2: Only conclusions II and III follow
Option 3: Only conclusions I and II follow
Option 4: Only conclusions I and III follow
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Correct Answer: Only conclusions I and II follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion I:
Some boys are males – From the above Venn diagram, it is clear that some part of the circle of boys lies inside the circle of males and some part lies outside the circle of males. Therefore, this conclusion follows.
Conclusion II:
Some teachers are students – From the above Venn diagram, it is clear that some part of the circle of teachers lies inside the circle of students and some part lies outside the circle of students. Therefore, this conclusion follows.
Conclusion III:
All males are students – From the above Venn diagram, it is clear that there is no direct relation between males and students. Therefore, this conclusion does not follow.
So, only conclusions I and II follow. Hence, the third option is correct.
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