A loss of electrons is known as oxidation, and a gain of electrons is known as reduction. Displacement reactions involving halogens involve a transfer of electrons, and reduction and oxidation happen simultaneously. For example, in the example here, chorine is reduced and iodine is oxidised.
'redox' is short for 'reduction and oxidation' and, as displacement reactions involving halogens involve the transfer of electrons, they are redox reactions.
NOTE: a good way to remember which is oxidation and which is reduction with the anagram 'O.I.L.R.I.G' (Oxidation.Is.Loss.Reduction.Is.Gain)
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