Answer :
Let us analyze each statement given the set [tex]\( A = \{1, 2, 3\} \)[/tex].
### Statement 1: [tex]\( \{1\} \in A \)[/tex]
- Here, [tex]\( \{1\} \)[/tex] is a set containing a single element, the number 1.
- For [tex]\( \{1\} \)[/tex] to be an element of [tex]\( A \)[/tex], the entire set [tex]\( \{1\} \)[/tex] (and not just the element 1) must be present in [tex]\( A \)[/tex].
- In this case, [tex]\( A \)[/tex] consists of the numbers 1, 2, and 3, not the set [tex]\( \{1\} \)[/tex].
- Hence, [tex]\( \{1\} \notin A \)[/tex]. This statement is incorrect.
### Statement 2: [tex]\( 1 \in A \)[/tex]
- This statement checks if the element 1 is a member of the set [tex]\( A \)[/tex].
- Upon examining [tex]\( A \)[/tex], we see that indeed, [tex]\( 1 \)[/tex] is one of the elements in [tex]\( A \)[/tex].
- Therefore, [tex]\( 1 \in A \)[/tex]. This statement is correct.
### Statement 3: [tex]\( \{1, 2\} \in A \)[/tex]
- Here, [tex]\( \{1, 2\} \)[/tex] is a set containing the elements 1 and 2.
- For [tex]\( \{1, 2\} \)[/tex] to be an element of [tex]\( A \)[/tex], the entire set [tex]\( \{1, 2\} \)[/tex] must be present in [tex]\( A \)[/tex].
- Since [tex]\( A \)[/tex] only contains the elements 1, 2, and 3 individually, not the set [tex]\( \{1, 2\} \)[/tex] as a whole, [tex]\( \{1, 2\} \notin A \)[/tex].
- Hence, this statement is incorrect.
### Statement 4: [tex]\( 3 \notin A \)[/tex]
- This statement checks if the element 3 is not a member of the set [tex]\( A \)[/tex].
- Looking at the set [tex]\( A \)[/tex], we see that 3 is indeed one of the elements.
- Thus, [tex]\( 3 \in A \)[/tex], meaning [tex]\( 3 \notin A \)[/tex] is false.
- Therefore, this statement is incorrect.
After evaluating all the statements, the only correct one is:
[tex]\[ \boxed{1 \in A} \][/tex]
### Statement 1: [tex]\( \{1\} \in A \)[/tex]
- Here, [tex]\( \{1\} \)[/tex] is a set containing a single element, the number 1.
- For [tex]\( \{1\} \)[/tex] to be an element of [tex]\( A \)[/tex], the entire set [tex]\( \{1\} \)[/tex] (and not just the element 1) must be present in [tex]\( A \)[/tex].
- In this case, [tex]\( A \)[/tex] consists of the numbers 1, 2, and 3, not the set [tex]\( \{1\} \)[/tex].
- Hence, [tex]\( \{1\} \notin A \)[/tex]. This statement is incorrect.
### Statement 2: [tex]\( 1 \in A \)[/tex]
- This statement checks if the element 1 is a member of the set [tex]\( A \)[/tex].
- Upon examining [tex]\( A \)[/tex], we see that indeed, [tex]\( 1 \)[/tex] is one of the elements in [tex]\( A \)[/tex].
- Therefore, [tex]\( 1 \in A \)[/tex]. This statement is correct.
### Statement 3: [tex]\( \{1, 2\} \in A \)[/tex]
- Here, [tex]\( \{1, 2\} \)[/tex] is a set containing the elements 1 and 2.
- For [tex]\( \{1, 2\} \)[/tex] to be an element of [tex]\( A \)[/tex], the entire set [tex]\( \{1, 2\} \)[/tex] must be present in [tex]\( A \)[/tex].
- Since [tex]\( A \)[/tex] only contains the elements 1, 2, and 3 individually, not the set [tex]\( \{1, 2\} \)[/tex] as a whole, [tex]\( \{1, 2\} \notin A \)[/tex].
- Hence, this statement is incorrect.
### Statement 4: [tex]\( 3 \notin A \)[/tex]
- This statement checks if the element 3 is not a member of the set [tex]\( A \)[/tex].
- Looking at the set [tex]\( A \)[/tex], we see that 3 is indeed one of the elements.
- Thus, [tex]\( 3 \in A \)[/tex], meaning [tex]\( 3 \notin A \)[/tex] is false.
- Therefore, this statement is incorrect.
After evaluating all the statements, the only correct one is:
[tex]\[ \boxed{1 \in A} \][/tex]
