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Statements: All Rackets Are Jackets. No Cow is Cat. Only Cats Are Dogs. Conclusions: Some Rackets Are Not Cats. Some Cats Are Jackets. No Dog is a Cow. - Logical Reasoning

MCQ

In the question, a few statements are followed by four conclusions numbered I, II, III and IV. Consider the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusion(s) and then decide which of the given conclusion(s) logically follow(s) from the given statements.

Statements: 

  1. All rackets are jackets.
  2. No cow is cat.
  3. Only cats are dogs.

Conclusions:

  1. Some rackets are not cats.
  2. Some cats are jackets.
  3. Some rackets are cats.
  4. No dog is a cow.

Options

  • Only II and IV follow

  • Only either I or III and IV follow

  • Only III and IV follow

  • Only I and IV follow

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Solution

Only either I or III and IV follow
" only cats are dogs" implies "All dogs are cats." Now all dogs are cats + conversion of statements (B) gives conclusion IV [∵ A + E = E]. Hence, Conclusion IV follows. Again, since there is no common term between statement A and (B or C), We can't get any specific conclusion regarding 'racket' or 'jacket' and 'cat'.
Therefore, neither conclusion I nor II nor conclusion III follows.
But Since conclusion, I and conclusion III make a complementary pair either conclusion I or conclusion III follows.

Concept: Syllogism
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