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Logical Deduction

Directions to SolveIn each of the following questions, three statements are given followed by four conclusions numbered I, II, III and TV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Q1:

Statements: No tree is fruit. All fruits are stones. All stones are rains. Conclusions:
  1. No stone is tree.
  2. No rain is tree.
  3. Some rains are fruits.
  4. Some rains are trees.

A Only either II or III, and I follow

B None follows

C Only either II or IV, and III follow

D All follow

E None of these

ANS:C - Only either II or IV, and III follow

Explanation: No tree is fruit. All fruits are stones. Since the middle term 'fruits' is distributed twice, the conclusion must be particular. Since one premise is negative, the conclusion must be negative. So, it follows that 'Some stones are not trees'. All fruits are stones. All stones are rains. Clearly, it follows that 'All fruits are rains'. III is the converse of this conclusion and so it holds. No tree is fruit, All fruits are rains. As discussed above, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some rains are not trees'. However, II and IV involve only the extreme terms and form a complementary pair. Thus, either II or IV follows.



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