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. [tex]\(0\)[/tex]
E. [tex]\(1\)[/tex]
F. [tex]\(2\)[/tex]



Answer :

To determine the numbers that are in the domain of the relation [tex]\( R = \{ (-3, -2), (-3, 0), (-1, 2), (1, 2) \} \)[/tex], we need to identify all of the unique first elements of the ordered pairs in [tex]\( R \)[/tex].

Let's examine each pair:

1. The first pair is [tex]\((-3, -2)\)[/tex]:
- The first element is [tex]\(-3\)[/tex].

2. The second pair is [tex]\((-3, 0)\)[/tex]:
- The first element is [tex]\(-3\)[/tex].

3. The third pair is [tex]\((-1, 2)\)[/tex]:
- The first element is [tex]\(-1\)[/tex].

4. The fourth pair is [tex]\((1, 2)\)[/tex]:
- The first element is [tex]\(1\)[/tex].

Next, we collect all the unique first elements from these pairs:

- From [tex]\((-3, -2)\)[/tex], we have [tex]\(-3\)[/tex].
- From [tex]\((-3, 0)\)[/tex], we again have [tex]\(-3\)[/tex] (which is already noted).
- From [tex]\((-1, 2)\)[/tex], we have [tex]\(-1\)[/tex].
- From [tex]\((1, 2)\)[/tex], we have [tex]\(1\)[/tex].

The unique first elements (i.e., the domain) are:

[tex]\[ \{-3, -1, 1\} \][/tex]

So, the numbers that are in the domain from the list provided are:

[tex]\[ -3, -1, 1 \][/tex]