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Parallelograms Equal F₂∪F₃∪F₄∪F₁ for Quadrilateral Sets | JEE

JEE Maths question with a full step-by-step solution.

Question
Let F1F_1 be the set of parallelograms, F2F_2 the set of rectangles, F3F_3 the set of rhombuses, F4F_4 the set of squares and F5F_5 the set of trapeziums in a plane. Then F1F_1 may be equal to:
AF2∩F3F_2 \cap F_3
BF3∩F4F_3 \cap F_4
CF2∪F5F_2 \cup F_5
DF2∪F3∪F4∪F1F_2 \cup F_3 \cup F_4 \cup F_1correct
Solution
Every rectangle, rhombus and square is a parallelogram, but a trapezium is not:
F2⊆F1,F3⊆F1,F4⊆F1.F_2 \subseteq F_1, \quad F_3 \subseteq F_1, \quad F_4 \subseteq F_1.
∴F2∪F3∪F4∪F1=F1.\therefore F_2 \cup F_3 \cup F_4 \cup F_1 = F_1.
 Correct answer: (4)
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