3. Let $S=\left\{(x, y) \mid x^{2}-y^{2}=\right.$ odd, $\left.x, y \in \mathbf{R}\right\}, T=\left\{(x, y) \mid \sin \left(2 \pi x^{2}\right)-\sin \left(2 \pi y^{2}\right)=\right.$ $\left.\cos \left(2 \pi x^{2}\right)-\cos \left(2 \pi y^{2}\right), x, y \in \mathbf{R}\right\}$, then
A. $S \varsubsetneqq T$
B. $T \varsubsetneqq S$
C. $S=T$
D. $S \cap T=\varnothing$
3. For the set $T$, $\sin \left(2 \pi x^{2}\right)-\cos \left(2 \pi x^{2}\right)=\sin \left(2 \pi y^{2}\right)-\cos \left(2 \pi y^{2}\right) \Leftrightarrow \sin \left(2 \pi x^{2}-\frac{\pi}{4}\right)=$ $\sin \left(2 \pi y^{2}-\frac{\pi}{4}\right) \Leftrightarrow\left(2 \pi x^{2}-\frac{\pi}{4}\right)-\left(2 \pi y^{2}-\frac{\pi}{4}\right)=2 k \pi$ or $\left(2 \pi x^{2}-\frac{\pi}{4}\right)+\left(2 \pi y^{2}-\frac{\pi}{4}\right)=(2 k+1) \pi$, $k \in \mathbf{Z} \Leftrightarrow x^{2}-y^{2}=k$ or $x^{2}+y^{2}-k=\frac{3}{4}, k \in \mathbf{Z}$. Therefore, we know $S \subset T$.