It is known that neutrinos from supernova (SN) bursts can potentially give rise to nuclear recoil (NR) signals arising from the neutral current (NC) process of coherent elastic neutrino-nucleus scattering ($\mathrm{CE}\ensuremath{\nu}\mathrm{NS}$) interactions of the neutrinos with xenon nuclei in future, large (multiton scale) liquid xenon (LXe) detectors employed for dark matter searches, depending on the SN progenitor mass and distance to the SN. In this paper, we show that the same detectors will also be sensitive to inelastic charged-current (CC) interactions of the SN electron neutrinos (${\ensuremath{\nu}}_{e}\mathrm{CC}$) with xenon nuclei. Such interactions, while creating an electron in the final state, also leave the postinteraction target nucleus in an excited state, the subsequent deexcitation of which produces, among other particles, $\ensuremath{\gamma}$ rays and neutrons. The electron and deexcitation $\ensuremath{\gamma}$ rays will give ``electron recoil'' (ER) type signals, while the deexcitation neutrons---the so-called ``neutrino-induced neutrons'' (${\ensuremath{\nu}}_{e}\mathrm{In}$)---produce, through their multiple scattering on the xenon nuclei, further xenon nuclear recoils that will also give NR signals (in addition to those produced through the $\mathrm{CE}\ensuremath{\nu}\mathrm{NS}$ interactions). We discuss the observable scintillation and ionization signals associated with SN neutrino-induced $\mathrm{CE}\ensuremath{\nu}\mathrm{NS}$ and ${\ensuremath{\nu}}_{e}\mathrm{CC}$ events in a generic LXe detector and argue that upcoming, sufficiently large LXe detectors should be able to detect both these types of events due to neutrinos from reasonably close-by SN bursts. We also note that since the total CC-induced ER and NR signals receive contributions predominantly from ${\ensuremath{\nu}}_{e}\mathrm{CC}$ interactions while the $\mathrm{CE}\ensuremath{\nu}\mathrm{NS}$ contribution comes from NC interactions of all six species of neutrinos, identification of the ${\ensuremath{\nu}}_{e}\mathrm{CC}$ and $\mathrm{CE}\ensuremath{\nu}\mathrm{NS}$ origin events may offer the possibility of extracting useful information about the distribution of the total SN explosion energy going into different neutrino flavors.
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