% https://alfurka.github.io/quick-tikz/
\def \circleA {(0.5,0) circle [radius=1.5]}
\def \circleB {(0,-0.5) circle [radius=1.5]}

\begin{tikzpicture}[scale=2,background rectangle/.style={fill=white}, show background rectangle]
  % Axis
  \draw (-2.5,0) -- (2.5,0);
  \draw (0,-2.5) -- (0,2.5);
  \draw[step=0.5,gray,very thin] (-2.4,-2.4) grid (2.4,2.4);

  % Main shapes
  \draw[blue] \circleA;
  \draw[red] \circleB;

  % Intersection
  \begin{scope}
    \clip \circleA;
    \draw[pattern=crosshatch, even odd rule] \circleA \circleB;
  \end{scope}
\end{tikzpicture}