2 Proposition $p$: If $a, b \in \mathbf{R}$, then $|a+b|<1$ is a sufficient but not necessary condition for $|a|+|b|<1$; Proposition $q$: The domain of the function $y=\sqrt{|x+1|-2}$ is $(-\infty,-3] \cup[1$, $+\infty)$, then $($.
(A) “ $p$ or $q$ ” is a false proposition
(B) “ $p$ and $q$ ” is a true proposition
(C) $p$ is a true proposition, $q$ is a false proposition
(D) $p$ is a false proposition, $q$ is a true proposition
(2) Since $|a+b| \leqslant |a| + |b|$, therefore $|a+b| < 1$ is a necessary but not sufficient condition for $|a| + |b| < 1$, so proposition $p$ is false; from $|x+1| - 2 \geqslant 0$, we get $x \leqslant -3$ or $x \geqslant 1$, so proposition $q$ is true. Hence, the answer is D.