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The set is equal to

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Suppose A₁, A₂,...,A₃₀ are thirty sets each having 5 elements and B₁, B₂,...,B_n are n sets each with 3 elements, let and each element of S belongs to exactly 10 of the and exactly 9 of the , then n is equal to

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Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of m and n are respectively.

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For any two sets A and B, is equal to

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Let F₄ be the set of all parallelograms, F₂ the set of all rectangles, F₃ the set of all rhombuses, F₄ the set of all squares and F₅ the set of trapeziums in a plane. Then F₁ may be equal to