= Solution
{c}
Choose the four basis-spin signs as $(+,-,-,+)$ in the order of positions listed in the source; reversing all signs changes no diffraction intensity. Apart from the common <magnetic form factor> and perpendicular-moment factor, the <magnetic structure factor> is
$$
\begin{aligned}
F_M(hkl)&=m[e^{i\pi h}-e^{i\pi k}-e^{i\pi(h+l)}+e^{i\pi(k+l)}]\\
&=m[(-1)^h-(-1)^k][1-(-1)^l].
\end{aligned}
$$
The first factor is nonzero exactly when $h$ and $k$ have opposite parity, and the second exactly when $l$ is odd. Thus the magnetic Bragg peaks require
$$
\boxed{h+k=2n+1,\qquad l=2m+1.}
$$
When both conditions hold, $|F_M|=4|m|$ before geometric and magnetic-form-factor weights. These are magnetic selection rules for the antiferromagnetic component, not conditions forbidding all nuclear diffraction at other indices.
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