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Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statements. Statements: All waters are liquids. All liquids are juices. All juices are fruits. Conclusions: (I) All waters are fruits. (II) Some fruits are liquids.
Both conclusions (I) and (II) follow.
Only conclusion (I) follows.
Only conclusion (II) follows.
Neither conclusion (I) nor (II) follows.
Both conclusions (I) and (II) follow.
Since the statements are all 'All A are B' type, visualize them as nested circles: Water inside Liquid inside Juice inside Fruit. Any inner set is automatically a subset of any outer set.
Since the statements are all 'All A are B' type, visualize them as nested circles: Water inside Liquid inside Juice inside Fruit. Any inner set is automatically a subset of any outer set.
Establish Relationships
Statements: (1) Water is subset of Liquid, (2) Liquid is subset of Juice, (3) Juice is subset of Fruit. Combined: Water is subset of Liquid, which is subset of Juice, which is subset of Fruit.
Analyze Conclusion (I)
Since Water is contained within the Fruit set (Water subset of Liquid subset of Juice subset of Fruit), it is logically certain that 'All Waters are Fruits'.
Analyze Conclusion (II)
Since all Liquids are Fruits, at least some portion of Fruits must contain Liquids. Thus, 'Some Fruits are Liquids' is logically true.
B: Incorrect because it ignores Conclusion II. C: Incorrect because it ignores Conclusion I. D: Incorrect because both conclusions are logically valid derivatives of the nested set structure.
A is correct because the transitive property of 'All' sets (Water < Liquid < Juice < Fruit) confirms both the total inclusion of water in fruit and the partial intersection of fruit with liquids.
In 'All A are B' problems, always draw concentric circles. If the conclusion moves from the innermost circle to the outermost, it is always true; if it moves from outermost to innermost, it is only true if 'some' or 'all' is implied correctly.
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