7. For a metric space (X, d), boundary of a set A is defined as bdA...

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7. For a metric space (X, d), boundary of a set A is defined as bdA = clAnd(X-A). Prove each of the following for a set A: (i) The bdA is a closed set. (ii) A is closed if and only if bdA CA. (iii) clA = Aº U bd.A. 8. Describe the boundary of Q the set of rational numbers, considered as a subset of the set of Reals with usual metric. 7. For a metric space (X, d), boundary of a set A is defined as bdA = clAnd(X-A). Prove each of the following for a set A: (i) The bdA is a closed set. (ii) A is closed if and only if bdA CA. (iii) clA = Aº U bd.A. 8. Describe the boundary of Q the set of rational numbers, considered as a subset of the set of Reals with usual metric.