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

F_{2} \cap F_{3}

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F_{3} \cap F_{4}

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F_{2} \cup F_{5}

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F_{2} \cup F_{3} \cup F_{4} \cup F_{1}

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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
$F_{2} \subset F_{1}$ , $F_{3} \subset F_{1}$ , $F_{4} \subset F_{1}$
$∴$ $F_{1} = F_{1} \cup F_{2} \cup F_{3} \cup F_{4}$ .

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