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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: All doors are roads. No road is fruit. Some flowers are doors. Conclusions:
  1. Some fruits are doors.
  2. Some fruits are flowers.
  3. Some roads are flowers.
  4. No fruit is flower.

A Only either II or III, and IV follow

B Only either II or IV, and III follow

C Only either II or IV, and I follow

D Only either II or IV follows

E All follow

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

Explanation: All doors are roads. No road is fruit. Since both the premises are universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, it follows that 'No door is fruit.' Some flowers are doors. All doors are roads. Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some flowers are roads'. Ill is the converse of this conclusion and so it holds. Some flowers are roads. No road is fruit. 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 flowers are not fruits'. II and IV involve the extreme terms and form a complementary pair. Thus, either II or IV follows.



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