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
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
Updated On: Jul 6, 2022
- $F_2 \cap F_3$
- $F_3 \cap F_4$
- $F_2 \cup F_5$
- $F_1 \cup F_2 \cup F_3 \cap F_4$
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The Correct Option is D
Solution and Explanation
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
$F_2 \subset F_1$, $F_3 \subset F_1$, $F_4 \subset F_1$
$\therefore F_1 = F_1 \cup F_2 \cup F_3 \cup F_4$
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Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
Representation of Sets
There are three basic notation or representation of sets are as follows:
Statement Form: The statement representation describes a statement to show what are the elements of a set.
- For example, Set A is the list of the first five odd numbers.
Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
- For example represent the set of vowels in roster form.
A={a,e,i,o,u}
Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
- For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
- Sometimes a ":" is used in the place of the "|".