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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: Some pearls are stones. Some stones are diamonds. No diamond is a gem. Conclusions:
  1. Some gems are pearls.
  2. Some gems are diamonds.
  3. No gem is a diamond.
  4. No gem is a pearl.

A Only I and II follow

B Only III and IV follow

C Only either I or IV and either II or III follow

D Only III and either I or IV follow

E None of these

ANS:D - Only III and either I or IV follow

Explanation: III is the converse of the third premise and so it holds. Some pearls are stones. Some stones are diamonds. Since both the premises are particular, no definite conclusion follows. Some stones are diamonds. No diamond is a gem. Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some stones are not gems'. However, I and IV involve the extreme terms of the three premises and form a complementary pair, Thus, either I or IV follows.



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