Let \(F_1\) be the set of all parallelograms, \(F_2\) the set of all rectangles, \(F_3\) the set of all rhombuses, \(F_4\) the set of all squares and \(F_5\) the set of all trapeziums in a plane. Then \(F_1\) may be equal to
(a) \(F_2\cap F_3\)
(b) \(F_3\cap F_4\)
(c) \(F_2\cup F_3\)
(d) \(F_2\cup F_3\cup F_4\cup F_1\)
Solution
Every rectangle is a parallelogram.
Every rhombus is also a parallelogram.
Every square belongs to both rectangles and rhombuses.
Therefore,
\[ F_2\subseteq F_1,\qquad F_3\subseteq F_1,\qquad F_4\subseteq F_1 \]
Hence,
\[ F_2\cup F_3\cup F_4\cup F_1=F_1 \]
Answer
\[ \boxed{F_2\cup F_3\cup F_4\cup F_1} \]
Correct option: (d)