Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true even if they seem to be at variance from commonly known facts. Decide which conclusion(s) logically follows from the given statements.
Statement :
No Pigeon is a Panduk.
Some Panduk are sparrows.
All sparrows are birds.
Conclusion:
(I) Some sparrows are not pigeons.
(II) Some sparrows are Panduk.
(III) Some birds are Panduk.
- AOnly conclusion । follows
- BEither conclusion । follows or Conclusion III follows
- CAll conclusions I, II and III follow
- DOnly conclusion II follows
Solution & Step-by-step Explanation
Let's convert the given statements into set representations:
Pigeon∩Panduk=∅
Panduk∩Sparrow
=∅
Sparrow⊆Birds
Let's evaluate each conclusion:
Conclusion I: "Some sparrows are not pigeons." The sparrows that are Panduk cannot be pigeons because no Panduk is a pigeon. This is absolutely true and follows.
Conclusion II: "Some sparrows are Panduk." Given directly by statement 2 ("Some Panduk are sparrows"), which implies its converse is also true. This follows.
Conclusion III: "Some birds are Panduk." Since all sparrows are birds and some sparrows are Panduk, the sparrows that are Panduk are also birds. Thus, those birds are Panduk. This follows.
Since all three conclusions I, II, and III follow, option C is correct.
Pigeon∩Panduk=∅
Panduk∩Sparrow
=∅
Sparrow⊆Birds
Let's evaluate each conclusion:
Conclusion I: "Some sparrows are not pigeons." The sparrows that are Panduk cannot be pigeons because no Panduk is a pigeon. This is absolutely true and follows.
Conclusion II: "Some sparrows are Panduk." Given directly by statement 2 ("Some Panduk are sparrows"), which implies its converse is also true. This follows.
Conclusion III: "Some birds are Panduk." Since all sparrows are birds and some sparrows are Panduk, the sparrows that are Panduk are also birds. Thus, those birds are Panduk. This follows.
Since all three conclusions I, II, and III follow, option C is correct.