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. $F_1 \cup F_2 \cup F_3 \cap F_4$

Answer 1

Answer: (D)

$F_1 \cup F_2 \cup F_3 \cap F_4$

Answer 2

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 $F_2 \subset F_1$, $F_3 \subset F_1$, $F_4 \subset F_1$ $\therefore F_1 = F_1 \cup F_2 \cup F_3 \cup F_4$