Long duration Gamma-Ray Bursts (GRBs) have eight luminosity relations where observable burst properties can yield the burst luminosity and hence distance. This turns GRBs into useful tools of cosmology. Recently, two tests have been proposed (by Nakar & Piran and by Li) for which one of the eight relations is claimed to have significant problems. In this paper, we generalize these tests and apply them to all eight GRB luminosity relations. (a) All eight relations pass the Nakar & Piran test

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... r accounting for the uncertainties on the data and the dispersions of the correlations. (b) All eight relations are good when the GRB redshifts are known, for example for calibration of the relations and for GRB Hubble diagram purposes. (c) We confirm the earlier results that the E_gamma,iso - E_peak Amati relation must produce very large error bars whenever an unknown redshift being sought is >1.4. (d) The E_gamma - E_peak relation of Ghirlanda et al. must produce very large error bars whenever an unknown redshift being sought is >3.4. (e) The other six relations have no problem at all from the ambiguity test of Li.