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:
No sheet is a pillow.
Some pillows are blankets.
All blankets are rugs.
Conclusions:
I. Some pillows are rugs.
II. All blankets can never be sheets.
III. Some rugs are sheets.
Option 1: Only conclusion III follows
Option 2: Only conclusion II follows
Option 3: Only conclusions II and III follow
Option 4: Only conclusions I and II follow
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Correct Answer: Only conclusions I and II follow
Solution : According to the given statements, the Venn diagram is as follows –
Let's analyse the conclusions –
Conclusion I:
Some pillows are rugs – From the Venn diagram, it is evident that the circles representing pillows and rugs overlap and have a part of their area in common. Thus, it can be concluded that some pillows are rugs.
Conclusion II:
All blankets can never be sheets – Since some blankets are pillows and no sheet is a pillow, therefore, blankets that are pillows can never be sheets. Thus, this conclusion follows.
Conclusion III:
Some rugs are sheets – The circles representing rugs and sheets may overlap. But this is not definite. Thus, this conclusion doesn’t follow.
So, only conclusions I and II follow. Hence, the fourth option is correct.
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