Given the relation

[tex]\[ R=\{(-3,-2),(-3,0),(-1,2),(1,2)\} \][/tex]

Select all numbers that are in the domain.

A. [tex]\(-3\)[/tex]

B. [tex]\(-2\)[/tex]

C. [tex]\(-1\)[/tex]

D. 0

E. 1

F. 2



Answer :

To determine the numbers that are in the domain of relation [tex]\( R = \{(-3,-2), (-3,0), (-1,2), (1,2)\} \)[/tex], follow these steps:

1. Understand the concept of the domain: The domain of a relation is the set of all first elements in the ordered pairs.

2. Identify the first elements (domain): Look at each ordered pair in the relation [tex]\( R \)[/tex] and extract the first component:
- For [tex]\((-3, -2)\)[/tex], the first element is [tex]\(-3\)[/tex].
- For [tex]\((-3, 0)\)[/tex], the first element is [tex]\(-3\)[/tex].
- For [tex]\((-1, 2)\)[/tex], the first element is [tex]\(-1\)[/tex].
- For [tex]\((1, 2)\)[/tex], the first element is [tex]\(1\)[/tex].

3. List the unique elements of the domain: Collect all distinct first elements from the pairs:
- The elements are [tex]\(-3\)[/tex], [tex]\(-3\)[/tex], [tex]\(-1\)[/tex], and [tex]\(1\)[/tex].
- Removing duplicates, we get the domain [tex]\(\{-3, -1, 1\}\)[/tex].

4. Match with the given numbers to identify those in the domain: The given numbers to select from are [tex]\(-3\)[/tex], [tex]\(-2\)[/tex], [tex]\(-1\)[/tex], [tex]\(0\)[/tex], [tex]\(1\)[/tex], and [tex]\(2\)[/tex].

5. Check each number against the domain:
- [tex]\(-3\)[/tex] is in the domain.
- [tex]\(-2\)[/tex] is not in the domain.
- [tex]\(-1\)[/tex] is in the domain.
- [tex]\(0\)[/tex] is not in the domain.
- [tex]\(1\)[/tex] is in the domain.
- [tex]\(2\)[/tex] is not in the domain.

Thus, the numbers that are in the domain are [tex]\( \boxed{-3, -1, 1} \)[/tex].