3. Given the point sets $A=\left\{(x, y) \left\lvert\,(x-3)^{2}+(y-4)^{2} \leqslant\left(\frac{5}{2}\right)^{2}\right.\right\}, B=\left\{(x, y) \mid(x-4)^{2}+(y-5)^{2}\right.$ $\left.>\left(\frac{5}{2}\right)^{2}\right\}$, the number of integer points (i.e., points with both coordinates as integers) in the point set $A \cap B$ is . $\qquad$
7
3.【Analysis and Solution】As shown in the figure, circles $E$ and $F$ intersect at points $M$ and $N$, and the entire figure is symmetrical about the line connecting the centers $E F$. Among them, $A \cap B$ is a crescent shape $S$ located at the lower left near the origin $O$. In $S$, the integer coordinates $x$ can be $1, 2, 3, 4$, and the integer coordinates $y$ can be $2, 3, 4, 5$. The axis of symmetry $E F$ passes through the crescent shape $S$, and it is calculated that it passes through only one integer point $C_{4}(2,3)$. In the crescent shape $S$, there are 3 grid points with an $x$-coordinate of 1:
$$
C_{1}(1,5), \quad C_{2}(1,4), \quad C_{3}(1,3) \text {. }
$$

The axis-symmetric points of these three points are, in order,
$$
C_{5}(2,2), \quad C_{6}(3,2), \quad C_{7}(4,2) \text {. }
$$

Therefore, there are a total of 7 integer points.