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4. Let H be a subgroup of a group G and let a, b e H. Using the definition of cosets, prove that Ha= Hb if and only if ab-EH.

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* Let H be a sub group of G First we will prove that На = H аен ut Ha=t Ha=t До я еен , eqe На еа ен conversly ut Заен a CH ,Now, we come to our proof ut Ha=Hb. = (Ha) b = (Hb) bt Habt - He Hast=H - abtEH completes the prool using 1 Hence

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