Question

Which of the following sets are equal?
$A=\{x:x\in N,x < 3\}$
$B=\{1,2\}$
$C=\{3,1\}$
$D=\{x:x\in N,\text{ }x\text{ is odd, }x < 5\}$
$E=\{1,2,1,1\}$
$F=\{1,1,3\}$

Answer 1

Hint: In order to solve this question, we need to first convert the given sets to their standard roaster form. Then you need to compare all the sets to check whether they are equal or not. Remember for two sets to be equal the number of elements is equal and all the elements are the same.

Complete step-by-step answer:

Before starting with the solution, let us discuss different symbols and operations related to sets.
Union: The union (denoted by $\cup $ ) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other.
Intersection: The intersection of two sets has only the elements common to both sets. If an element is in just one set it is not part of the intersection. The symbol is an upside down $\cap $ .
Two sets are said to be equal if they have the all there elements equal.

Now let us start with the solution to the question. First, we let us convert set A to roster form. It is given that $A=\{x:x\in N,x<3\}$ . So, the possible values of x are 1 and 2. Therefore, we can say that set $A=\left\{ 1,2 \right\}$ .
Now let us start with the conversion set D to roster form. It is given that $D=\{x:x\in N,\text{ }x\text{ is odd, }x<5\}$ . So, the possible values of x are 1 and 3. Therefore, we can say that set $D=\left\{ 1,3 \right\}$ .
Also, repetition in the roaster form of the set doesn’t signify anything. So, if set X={a,b,b,c} then set X can also be written as: X={a,b,c}. So, our sets are:
$A=\{1,2\}$
$B=\{1,2\}$
$C=\{3,1\}$
$D=\{1,3\}$
$E=\{1,2\}$
$F=\{1,3\}$
Therefore, we can conclude that set A, B and E are equal sets and set C, D and F are equal sets.

Note: We have used the fact that when the two sets are said to be equal, and also the definition of the given terms are also useful. One must memorize the definition so that there can be no mistake in the future. This is a simple question, and so the chance of making silly mistakes in a hurry to solve it are also higher. Also, be careful that the order of terms of the sets doesn’t matter for two sets to be equal. For example: set A={1,2} and set B={2,1} are equal sets.