If $A=\{3,5,7\}$ and $B=\{1,2,3,5\}$, then $A \times B \cap B \times A$ is equal to

The set $A \times B$ consists of all ordered pairs $(a, b)$ where $a \in A$ and $b \in B$. Given $A = \{3, 5, 7\}$ and $B = \{1, 2, 3, 5\}$, the elements of $A \times B$ are pairs $(a, b)$ such that $a \in \{3, 5, 7\}$ and $b \in \{1, 2, 3, 5\}$.

The set $B \times A$ consists of all ordered pairs $(b, a)$ where $b \in B$ and $a \in A$. The elements of $B \times A$ are pairs $(b, a)$ such that $b \in \{1, 2, 3, 5\}$ and $a \in \{3, 5, 7\}$.

The intersection $A \times B \cap B \times A$ contains pairs $(x, y)$ that belong to both $A \times B$ and $B \times A$. This implies $x \in A$ and $x \in B$, and $y \in A$ and $y \in B$.

The intersection of sets $A$ and $B$ is $A \cap B = \{3, 5, 7\} \cap \{1, 2, 3, 5\} = \{3, 5\}$.

Therefore, the elements of $A \times B \cap B \times A$ are pairs $(x, y)$ where $x \in \{3, 5\}$ and $y \in \{3, 5\}$.

Listing these pairs, we get $\{(3, 3), (3, 5), (5, 3), (5, 5)\}$.

Answer: $\{(3,3),(3,5),(5,3),(5,5)\}$