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If [tex]A =\{2,3,5\}[/tex] and [tex]B=\{1,4\}[/tex], what is the value of [tex]n ( A \cap B )[/tex]?

A. [tex]\rho[/tex]
B. 2
C. 0


Sagot :

To determine the value of [tex]\( n(A \cap B) \)[/tex], we need to find the number of elements in the intersection of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex].

Step-by-step, we follow these steps:

1. Identify the elements in set [tex]\( A \)[/tex] and set [tex]\( B \)[/tex]:
[tex]\[ A = \{2, 3, 5\} \][/tex]
[tex]\[ B = \{1, 4\} \][/tex]

2. Find the intersection of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex]: The intersection [tex]\( A \cap B \)[/tex] contains all elements that are both in [tex]\( A \)[/tex] and in [tex]\( B \)[/tex].

In this case, we check each element of [tex]\( A \)[/tex] to see if it is also in [tex]\( B \)[/tex]:

- [tex]\( 2 \)[/tex] is in [tex]\( A \)[/tex] but not in [tex]\( B \)[/tex].
- [tex]\( 3 \)[/tex] is in [tex]\( A \)[/tex] but not in [tex]\( B \)[/tex].
- [tex]\( 5 \)[/tex] is in [tex]\( A \)[/tex] but not in [tex]\( B \)[/tex].

Similarly, we can check the elements of [tex]\( B \)[/tex]:

- [tex]\( 1 \)[/tex] is in [tex]\( B \)[/tex] but not in [tex]\( A \)[/tex].
- [tex]\( 4 \)[/tex] is in [tex]\( B \)[/tex] but not in [tex]\( A \)[/tex].

None of the elements from set [tex]\( A \)[/tex] are present in set [tex]\( B \)[/tex]. Therefore, the intersection [tex]\( A \cap B \)[/tex] is the empty set:
[tex]\[ A \cap B = \emptyset \][/tex]

3. Determine [tex]\( n(A \cap B) \)[/tex]: [tex]\( n(A \cap B) \)[/tex] represents the number of elements in the intersection of [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. Since the intersection [tex]\( A \cap B \)[/tex] is an empty set, it contains no elements, so:
[tex]\[ n(A \cap B) = 0 \][/tex]

Hence, the value of [tex]\( n(A \cap B) \)[/tex] is [tex]\( 0 \)[/tex].

Therefore, the answer is:
[tex]\[ \boxed{0} \][/tex]

So, the correct option is:
[tex]\( (c) 0 \)[/tex]
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