Question

    Conclusions: Some Circles are Triangles. Some Squares

    being Circles is a possibility. All Triangles are Circles. In each of these questions, two Conclusions have been given followed by 5 sets of possible Statements. You have to take the given Conclusions to be true even if they seem to be at variance with the commonly known facts and then decide that the Conclusions logically follows for which of the given statements disregarding commonly known facts.
    A All Triangles are Cubes. All Cubes are Circles. Some Cuboids are Circles. Some Cuboids are Squares. Correct Answer Incorrect Answer
    B All Triangles are Cubes. All Cubes are Circles. All Cuboids are Circles. Some Cuboids are Squares. Correct Answer Incorrect Answer
    C Some Triangles are Cubes. Some Cubes are Circles. All Cuboids are Circles. Some Cuboids are Squares. Correct Answer Incorrect Answer
    D No Triangle is a Cube. No Cube is a Circle. All Cuboids are Circles. Some Cuboids are Squares. Correct Answer Incorrect Answer
    E None of the above Correct Answer Incorrect Answer

    Solution

    1) All Triangles are Cubes (A) + All Cubes are Circles (A) → All Triangles are Circles (A) → Conversion → Some Circles are Triangles (I). Hence conclusion I and III follow. Some Cuboids are Circles (I) → Conversion → Some Circles are Cuboids (I) + Some Cuboids are Squares (I) → Probable conclusion → Some Squares may be Circles (I). Hence conclusion II follows. Hence option 1 is correct. 2) All Triangles are Cubes (A) + All Cubes are Circles (A) → All Triangles are Circles (A) → Conversion → Some Circles are Triangles (I). Hence conclusion I and III follow. Some Cuboids are Squares (I) → Conversion → Some Squares are Cuboids (I) + All Cuboids are Circles (A) → Some Squares are Circles (I). Hence conclusion II does not follow. Hence option 2 is not correct. 3) Some Triangles are Cubes (I) + Some Cubes are Circles (I) → No conclusion. Hence neither conclusion I nor III follow. Some Cuboids are Squares (I) → Conversion → Some Squares are Cuboids (I) + All Cuboids are Circles (A) → Some Squares are Circles (I). Hence conclusion II does not follow. Hence option 3 is not correct. 4) No Triangle is a Cube (E) + No Cube is a Circle (E) → No conclusion. Hence neither conclusion I nor III follow. Some Cuboids are Squares (I) → Conversion → Some Squares are Cuboids (I) + All Cuboids are Circles (A) → Some Squares are Circles (I). Hence conclusion II does not follow. Hence option 4 is not correct.

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