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Answer :
We are given the sets
[tex]$$
A = \{\text{cake}, \text{cookie}, \text{pie}\} \quad \text{and} \quad B = \{\text{brownie}, \text{pie}, \text{scone}, \text{tart}\}.
$$[/tex]
The intersection of two sets, denoted by [tex]$A \cap B$[/tex], is the set of elements that are common to both [tex]$A$[/tex] and [tex]$B$[/tex]. In other words,
[tex]$$
A \cap B = \{ x \mid x \in A \text{ and } x \in B \}.
$$[/tex]
Now, we identify the common elements by comparing the elements in each set:
1. From set [tex]$A$[/tex], the element "cake" is not present in set [tex]$B$[/tex].
2. The element "cookie" from set [tex]$A$[/tex] is not present in set [tex]$B$[/tex].
3. The element "pie" appears in both set [tex]$A$[/tex] and set [tex]$B$[/tex].
Since "pie" is the only element found in both [tex]$A$[/tex] and [tex]$B$[/tex], we have
[tex]$$
A \cap B = \{\text{pie}\}.
$$[/tex]
Thus, the correct answer is
[tex]$$
\{\text{pie}\}.
$$[/tex]
[tex]$$
A = \{\text{cake}, \text{cookie}, \text{pie}\} \quad \text{and} \quad B = \{\text{brownie}, \text{pie}, \text{scone}, \text{tart}\}.
$$[/tex]
The intersection of two sets, denoted by [tex]$A \cap B$[/tex], is the set of elements that are common to both [tex]$A$[/tex] and [tex]$B$[/tex]. In other words,
[tex]$$
A \cap B = \{ x \mid x \in A \text{ and } x \in B \}.
$$[/tex]
Now, we identify the common elements by comparing the elements in each set:
1. From set [tex]$A$[/tex], the element "cake" is not present in set [tex]$B$[/tex].
2. The element "cookie" from set [tex]$A$[/tex] is not present in set [tex]$B$[/tex].
3. The element "pie" appears in both set [tex]$A$[/tex] and set [tex]$B$[/tex].
Since "pie" is the only element found in both [tex]$A$[/tex] and [tex]$B$[/tex], we have
[tex]$$
A \cap B = \{\text{pie}\}.
$$[/tex]
Thus, the correct answer is
[tex]$$
\{\text{pie}\}.
$$[/tex]
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Rewritten by : Jeany
