Logical Reasoning - Statement and Conclusion

In each of the questions below, there are two statements followed by three to four conclusions numbered as I, II, III, and IV. 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 follow from the given statements.

16. Statements
All magic are women.
All women are crazy.
Conclusions
I. All magic are crazy.
II. All crazy are magic.
III. Some crazy are magic.
IV. Some crazy are women.
Choices

  • Option : C
  • Explanation : Only three terms (magic, women, and crazy). No alignment is required as they are in the standard format.
    Now A + A = A.
    Conclusion: All magic is crazy. So statement I is correct. Its immediate inference is ‘Some crazy are magic’. It means the third statement is true.
    The converse of second statement ‘All women are crazy’ is ‘Some crazy are women’. So fourth conclusion is also true. Thus, option (c) is the answer.
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17. Statements
All cats are mammals.
No tigers are cats.
Conclusions

  • Option : D
  • Explanation : There are three terms. After alignment,
    Some mammals are cats.
    No cats are tigers.
    If we look at conclusions directly, the term ‘male teacher’ in the first conclusion and ‘women teachers’ and ‘present’ in the second conclusion are not mentioned in statements. So, option (d) is the answer.
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18. Statements
Some boxes are round.
All rounds are spheres.
Conclusions
I. Some boxes are spheres.
II. Some spheres are boxes.
III. Some spheres are round.
IV. All spheres are round.
Choices

  • Option : A
  • Explanation : I + A = I. The conclusion is some boxes are spheres which is I. This can be converted to some spheres are boxes, which is II. Conclusion III follows after converting all rounds are spheres. So, option (a) is the answer. Venn diagram solution:
    logical reasoning
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19. Statements
All books are clocks.
Some clocks are chips.
Conclusions
I. Some clocks are books.
II. No clocks are books.
III. Some books are chips.
IV. No books are chips.
Choices

  • Option : B
  • Explanation : They are in desired format A to B and B to C.
    All books are clocks (A-type)
    Some clocks are chips (I-type)
    A + I = No conclusion.
    Now, we can check first statement after immediate inference—Some clocks are books.
    Second statement after immediate inference—Some chips are clocks.
    So only conclusion I follows. Thus, option (b) is the answer.
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