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No, replacing the representative element g with another element g' from the same coset does not yield a different coset. If g' belongs to the same coset as g (i.e., $g' \in gH$), then the coset generated by g' is identical to the coset generated by g ($g'H = gH$).

Conditions: g and g' are both elements of the group G; g' and g belong to the same coset

No, replacing the representative element g with another element g' from the same coset does not yield a different coset. If g' belongs to the same coset as g (i.e., $g' \in gH$), then the coset generated by g' is identical to the coset generated by g ($g'H = gH$).

Conditions: g and g' are both elements of the group G; g' and g belong to the same coset