Directions: In the following question below some statements are given followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusions logically follows the given statements. Statements: All toy are doll. Some doll are white. Conclusions: I. No toy is white. II. Some doll are toy.
Directions: In the following question below some statements are given followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusions logically follows the given statements.
Statements: All toy are doll. Some doll are white.
Conclusions: I. No toy is white. II. Some doll are toy.
correct answer is: option a : Only conclusion II follows.
Explanation: Let's analyze the statements and conclusions using a Venn diagram approach.
Statements: * All toy are doll: This means the entire circle representing "toy" is inside the circle representing "doll." * Some doll are white: This means there is an overlap between the circle representing "doll" and the circle representing "white."
Conclusions: * I. No toy is white: This is not necessarily true. While it's *possible* that the "white" circle doesn't overlap with the "toy" circle, it's also possible that it *does* overlap. Since the statement "Some doll are white" allows for the possibility that these "doll" which are "white" are also "toy" (because "toy" is contained by "doll"), we cannot conclude that *no* "toy" is white. Therefore, conclusion I does not necessarily follow. * II. Some doll are toy: Since "All toy are doll", we know that all "toy" are inside the set of "doll". Thus, it logically follows that some of the "doll" are "toy". Therefore, conclusion II follows.
- Option a: This is the correct answer because conclusion II follows and conclusion I does not necessarily follow.
- Option b: This is incorrect because conclusion I does not necessarily follow.
- Option c: This is incorrect because conclusion II follows.
- Option d: This is incorrect because conclusion I does not necessarily follow.
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