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Question

Let $${ F }_{ 1 }$$ be the set of parallelograms, $${ F }_{ 2 }$$ be the set of rectangles, $${ F }_{ 3 }$$ be the set of rhombuses, $${ F }_{ 4 }$$ be the set of squares and $${ F }_{ 5 }$$ be the set of trapeziums in a plane. Then, $${ F }_{ 1 }$$ may be equal to


A
F2F3
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B
F3F4
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C
F2F5
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D
F2F3F4F1
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Solution

The correct option is D $${ F }_{ 2 }\cup { F }_{ 3 }\cup { F }_{ 4 }\cup { F }_{ 1 }$$
Given, $${ F }_{ 1 }=$$ the set of parallelograms
           $${ F }_{ 2 }=$$ the set of rectangles
           $${ F }_{ 3 }=$$ the set of rhombuses
           $${ F }_{ 4 }=$$ the set of squares
and     $${ F }_{ 5 }=$$ the set of trapeziums
By definition of parallelogram, opposite sides are equal and parallel. In rectangles, rhombuses and squares, all have opposite sides equal and parallel, therefore
           $${ F }_{ 2 }\subset { F }_{ 1 }$$,  $${ F }_{ 3 }\subset { F }_{ 1 }$$,  $${ F }_{ 4 }\subset { F }_{ 1 }$$
$$\therefore $$   $${ F }_{ 1 }={ F }_{ 1 }\cup { F }_{ 2 }\cup { F }_{ 3 }\cup { F }_{ 4 }$$.

Mathematics

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