  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  B
F3F4  C
F2F5  D
F2F3F4F1  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 squaresand     $${ F }_{ 5 }=$$ the set of trapeziumsBy 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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