Question:
Let F1 be the set of all parallelograms, F2 the set of all rectangles, F3 the set of all rhombuses, F4 the set of all squares and F5 the set of trapeziums in a plane. Then F1 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:
We know that every rectangle, rhombus and square in a plane is a parallelogram but every trapezium is not a parallelogram.
So, $F_{1}$ is either of $F_{1}$ or $F_{2}$ or $F_{3}$ or $F_{4}$.
$\therefore F_{1}=F_{1} \cup F_{2} \cup F_{3} \cup F_{4}$
Hence, the correct answer is option (d).