Sure, let's find the intersection of the two given sets [tex]\(P\)[/tex] and [tex]\(Q\)[/tex].
Recall that the intersection of two sets consists of elements that are present in both sets.
Given:
[tex]\[ P = \{0, 1, 2, 3\} \][/tex]
[tex]\[ Q = \{-3, -2, -1, 0\} \][/tex]
Step-by-step process:
1. Identify the elements of Set [tex]\(P\)[/tex]:
[tex]\[ P = \{0, 1, 2, 3\} \][/tex]
2. Identify the elements of Set [tex]\(Q\)[/tex]:
[tex]\[ Q = \{-3, -2, -1, 0\} \][/tex]
3. Compare each element of Set [tex]\(P\)[/tex] with each element of Set [tex]\(Q\)[/tex] to find common elements:
- The element [tex]\(0\)[/tex] is present in both sets [tex]\(P\)[/tex] and [tex]\(Q\)[/tex].
- The elements [tex]\(1, 2, 3\)[/tex] in Set [tex]\(P\)[/tex] are not present in Set [tex]\(Q\)[/tex].
- The elements [tex]\(-3, -2, -1\)[/tex] in Set [tex]\(Q\)[/tex] are not present in Set [tex]\(P\)[/tex].
4. List the common elements found in both sets:
The only common element is [tex]\(0\)[/tex].
So the intersection of sets [tex]\(P\)[/tex] and [tex]\(Q\)[/tex] is:
[tex]\[ P \cap Q = \{0\} \][/tex]
Therefore, the intersection of the sets [tex]\(P\)[/tex] and [tex]\(Q\)[/tex] is [tex]\(\{0\}\)[/tex].
