= Solution
With
$$
\partial_\mu=\left(\frac1c\frac{\partial}{\partial t},\nabla\right),
$$
the <electromagnetic field tensor> is the antisymmetric tensor
$$
\boxed{
F^{\mu\nu}
=\partial^\mu A^\nu-\partial^\nu A^\mu}.
$$
Under a Lorentz transformation $x'^\mu=\Lambda^\mu{}_\nu x^\nu$, the four-potential transforms as a four-vector and therefore
$$
\boxed{
F'^{\mu\nu}(x')
=\Lambda^\mu{}_\rho\Lambda^\nu{}_\sigma
F^{\rho\sigma}(x)}.
$$
\b[Thus $F$ is an antisymmetric rank-two <tensor> under <Lorentz transformation>[Lorentz transformations].]
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