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 toa F 2 - F 3b F 3 - F 4c F2UF3d F2UF3UF4UF1

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Byju's Answer

Standard VIII

Mathematics

Parallelogram

Let F1 be the...

Question

Let F₁ be the set of all parallelograms, F₂the set of all rectangles, F₃the set of all rhombuses, F₄the set of all squares and F₅the 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) $F_{2} \cup F_{3} \cup F_{4} \cup F_{1}$

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Solution

We know that every rectangle, rhombus and square in a plane is a parallelogram but every trapezium is not a parallelogram.

So, F₁ is either of F₁ or F₂ or F₃or F₄.

$∴ F_{1} = F_{1} \cup F_{2} \cup F_{3} \cup F_{4}$

Hence, the correct answer is option (d).

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