Exercise 2. If h : A → B is an injection and C C A, then h[A\C] = h[A] \ h[C]. Definition. Let S be the set of infinite binary sequences x = (x1, x2,.. Xn .), where x = {0, 1} for all n ≥ 0; and let E be the relation on S defined by x Ey there exists no E N such that xn = Yn for all n no. Exercise 3. Prove that E is an equivalence relation on S.

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