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We study two well-known SU(N) chiral gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. We give a detailed description of the global symmetry, including various discrete quotients. Recent work argues that these theories exhibit a subtle mod 2 anomaly, ruling out certain phases in which the theories confine without breaking their global symmetry, leaving a gapless composite fermion in the infra-red. We point out that no such anomaly exists. We furtherdoi:10.1007/jhep01(2022)112 fatcat:uhvfi7xbd5gmzaso7lwfq3qy7m