  We present the results of ROSAT All-Sky Survey observations of Seyfert and
IR-luminous galaxies from the Extended 12 Micron Galaxy Sample and the
optically-selected CfA Sample. Roughly half of the Seyferts (mostly Seyfert 1s)
have been fitted to an absorbed power-law model, yielding an average gamma of
2.26+-0.11 for 43 Seyfert 1s and 2.45+-0.18 for 10 Seyfert 2s, with both types
having a median value of 2.3.
  The soft X-ray (SXR) luminosity correlates with the 12um luminosity, with
Seyfert 1s having relatively more SXR emission than Seyfert 2s of similar
mid-infrared luminosities, by a factor of 1.6+-0.3. Several physical
interpretations of these results are discussed, including the standard unified
model for Seyfert galaxies. Infrared-luminous non-Seyferts are shown to have
similar distributions of SXR luminosity and X-ray-to-IR slope as Seyfert 2s,
suggesting that some of them may harbor obscured active nuclei (as has already
been shown to be true for several objects) and/or that the soft X-rays from
some Seyferts 2s may be non-nuclear.
  A SXR luminosity function (XLF) is calculated for the 12um sample, which is
well described by a single power-law with a slope of -1.75. The normalization
of this XLF agrees well with that of a HXR selected sample. Several of our
results, related to the XLF and the X-ray-to-IR relation are shown to be
consistent with the HXR observations of the 12um sample by Barcons et al.
