3. In the plane, there are three point sets $M, N, P: M=\{(x, y) \mid | x|+| y |<1\}$,
$$
\begin{array}{l}
N=\left\{(x, y) \left\lvert\, \sqrt{\left(x-\frac{1}{2}\right)^{2}+\left(y+\frac{1}{2}\right)^{2}}+\sqrt{\left(x+\frac{1}{2}\right)^{2}+\left(y-\frac{1}{2}\right)^{2}}<2 \sqrt{2}\right.\right\}, \\
P=\{(x, y) \mid | x+y|<1,| x|<1,| y \mid<1\} . \text { Then }
\end{array}
$$
A. $M \varsubsetneqq P \varsubsetneqq N$
B. $M \varsubsetneqq N \varsubsetneqq P$
C. $P \subsetneq N \subsetneq M$
D. None of A, B, C are true
Answer
As shown in the figure, the point set $M$ represents the square region $C D E F$, the point set $N$ represents the elliptical region with $M, N$ as foci, and the point set $P$ represents the hexagonal region $A C D B E F$. Therefore, we have $M \varsubsetneqq P \varsubsetneqq N$. So the answer is $A$.