We cross correlate the well-defined and very complete spectroscopic Main Galaxy Sample (MGS) of 156,000 bright (r<17.5 mag) galaxies from the SDSS with 2MASS sources to explore the nature and completeness of the 2MASS K-band selection of nearby galaxies. 2MASS detects 90% of the MGS brighter than r=17 mag. For r<16, 93.1% of the MGS is found in the 2MASS Extended Source Catalog (XSC). These detections span the representative range of optical and near-IR galaxy properties, but with a surface brightness-dependent bias to preferentially miss the most blue and low-concentration sources, consistent with the most morphologically late-type galaxy population. An XSC completeness of 97.5% is achievable at bright magnitudes, with blue LSBs being the only major source of incompleteness, if one follows our careful matching criteria and weeds out spurious SDSS sources. We conclude that the rapid drop in XSC completeness at r>16 reflects the sharp surface-brightness limit of the extended source detection algorithm in 2MASS. As a result, the r>16 galaxies found in the XSC are over-representative in red early types and under-representative in blue latetypes. At r>16 the XSC suffers an additional selection effect from the 2-3 spatial resolution limit of 2MASS. Therefore, 2MASS continues to detect 90% of of the MGS at 16<r<17, but with a growing fraction found in the Point Source Catalog (PSC) only. Overall, one third of the MGS is detected in the 2MASS PSC but not the XSC. A combined K<13.57 and r<16 selection provides the most representative inventory of galaxies in the local cosmos with near-IR and optical measurements, and 90.8% completeness. Using data from SDSS-DR2, this sample contains 19,156 galaxies with a median redshift of 0.052. (abridged)
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