Problem 27. State whether or not the following statement is false\" or \"true\". Justify your answer. (a) If X is a metric space and A C X is closed and bounded, then A is compact. (b) If X is a metric space and A C X is compact, then A is closed and bounded. (c) If (X,7) is a topological space and A C X is not open, then A is closed. (d) If {x,} is a convergent sequence in (X, .7 ), then every subsequence of {x,} is convergent in (X,.7)