Question : Directions: Three statements are given, followed by four conclusions numbered I, II, III, and IV. 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:
Some desks are trays.
Some trays are plates.
Some plates are desks.
Conclusions:
I. All desks are plates.
II. All plates are desks.
III. Some plates are trays.
IV. All trays are desks.
Option 1: Only conclusion III follows
Option 2: Only conclusion IV follows
Option 3: Only conclusion II follows
Option 4: Only conclusion I follows
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Correct Answer: Only conclusion III follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion I:
All desks are plates – From the above diagram, it is clear that only some parts of the circle that are desks overlap with the circle that is plate. So, only some desks are plates. Therefore, this conclusion does not follow.
Conclusion II:
All plates are desks – From the above diagram, it is clear that only some parts of the circle that are plates overlap with the circle that is desks. So, only some plates are desks. Therefore, this conclusion does not follow.
Conclusion III:
Some plates are trays – From the above diagram, it is clear that only some parts of the circle that are plates overlap with the circle that is trays. So, only some plates are trays. Therefore, this conclusion follows.
Conclusion IV:
All trays are desks – From the above diagram, it is clear that only some parts of the circle that are trays overlap with the circle that is desks. So, only some trays are desks. Therefore, this conclusion does not follow.
So, only conclusion III follows. Hence, the first option is correct.
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