Question

Let $F_1$ be 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 in the plane. Then $F_1$ may be equal to

• A. $F_2 \cap F_3$
• B. $F_3 \cap F_4$
• C. $F_2 \cup F_5$
• D. $F _{2} \cup F _{3} \cup F _{4} \cup F _{1}$

Answer 1

Answer: (D)

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
$ \begin{array}{l} 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} \end{array} $