1)If X is a complete metric space,then prove that the intersectionof a countable number of dense open subsets of X is dense in X.Is the result hold true if X is not complete ?Justify.

2)Let X be a normad space and Y be a closed subspace of X.Prove that X is a Banach space if and only if Y and X/Y are Banach spaces in the induced norm and the quotient norm respectively.

pls helllppp me on this 2 questions,anyone!!

Question

1)If X is a complete metric space,then prove that the intersectionof a countable number of dense open subsets of X is dense in X.Is the result hold true if X is not complete ?Justify.

2)Let X be a normad space and Y be a closed  subspace of X.Prove that X is a Banach space if and only if Y and X/Y are Banach spaces in the induced norm and the quotient norm respectively.  

pls helllppp me on this 2 questions,anyone!!