Let's analyze each of the options given in the context of the sets:
Given sets:
[tex]\[ A = \{1, 2, 3\} \][/tex]
[tex]\[ B = \{3, 2, 1\} \][/tex]
### Option 1: [tex]\(4 \in B\)[/tex]
This statement means that the number 4 is an element of set B. Looking at the elements of set B, we can see that the set B contains only the elements 1, 2, and 3. Therefore, the number 4 is not an element of B.
[tex]\[ \boxed{4 \notin B} \][/tex]
### Option 2: [tex]\(\varnothing \notin B\)[/tex]
This statement means that the empty set is not an element of set B. The empty set, denoted as [tex]\(\varnothing\)[/tex], is an important concept in set theory but it is not an element in B. Set B contains only the elements 1, 2, and 3, and there is no indication that the empty set is among its elements.
[tex]\[ \boxed{\varnothing \notin B} \][/tex]
### Option 3: A is an infinite set
An infinite set is a set that has an endless number of elements. To determine if set A is infinite, we count the number of elements in A. Set A has exactly three elements: 1, 2, and 3. Since the number of elements in set A is finite, it is not an infinite set.
[tex]\[ \boxed{\text{A is a finite set}} \][/tex]
### Option 4: [tex]\(A \subseteq B\)[/tex]
This statement means that set A is a subset of set B, meaning every element of A is also an element of B. Looking at the elements of both sets:
- Set A contains the elements: 1, 2, 3
- Set B contains the elements: 1, 2, 3
Since all elements of set A are present in set B, it can be concluded that A is indeed a subset of B.
[tex]\[ \boxed{A \subseteq B} \][/tex]
### Conclusion
Having analyzed all the options, the true statement is:
[tex]\[ \boxed{A \subseteq B} \][/tex]
