(A) Write any 2 sets by listing method and by rule method

(B) Write the following sets using the listing method

(i) All months in the Indian Solar Year

(ii) Letters in the word ‘COMPLEMENT’

Let's dive into the concept of sets, which are fundamental in mathematics. A set is simply a collection of distinct objects, considered as an object in its own right. We can represent sets in two primary ways: the listing method and the rule method. I'll explain both methods and then tackle your specific requests.

Creating Sets: Listing Method vs. Rule Method

1. Listing Method

In the listing method, we explicitly write down all the elements of the set, usually enclosed in curly braces. For example, if we want to create a set of the first three natural numbers, we would write it as:

• Set A = {1, 2, 3}

2. Rule Method

In the rule method, we define the set by a property that its members share. For instance, we can define the same set of natural numbers as:

• Set B = {x | x is a natural number and x < 4}

Examples of Sets

Set Creation

Now, let's create two sets using both methods:

Set 1: Even Numbers Less Than 10

Using the listing method, we can write:

• Set C = {2, 4, 6, 8}

Using the rule method, we can express it as:

• Set D = {x | x is an even number and x < 10}

Set 2: Prime Numbers Less Than 20

For the listing method, we have:

• Set E = {2, 3, 5, 7, 11, 13, 17, 19}

In the rule method, it can be defined as:

• Set F = {x | x is a prime number and x < 20}

Specific Sets Using the Listing Method

Months in the Indian Solar Year

Now, let's list the months in the Indian Solar Year. The Indian Solar Year typically consists of the following months:

• Set G = {Chaitra, Vaishakha, Jyeshtha, Ashadha, Shravana, Bhadrapada, Ashwin, Kartika, Margashirsha, Pushya, Magha, Phalguna}

Letters in the Word ‘COMPLEMENT’

Next, we can list the letters in the word 'COMPLEMENT'. Since we want distinct letters, we will avoid repetitions:

• Set H = {C, O, M, P, L, E, N, T}

In summary, we have successfully created sets using both the listing and rule methods, and we've also listed specific sets based on your request. Understanding how to represent sets is crucial in various areas of mathematics and helps in organizing information effectively.