Proof practice. (a) Convert this paragraph proof to a statement-reason proof. Please be sure to write which statement(s) each statement depends on. To show: If s is a string, every substring of a substring of s is a substring of s. Proof: Let y be a substring of s, that is, s=xyz for some x,z; and let v be a substring of y, that is, y=uvw for some u,w. Then s=xuvwz, so v is a substring of s. (b) Convert this statement-reason proof to a paragraph proof. To show: If w is a string, every prefix of a suffix of w is a suffix of a prefix of w. 1. v is a suffix of w Given 2. y is a prefix of v Given 3. x s.t. xv=w (1), def. suffix 4. z s.t. yz=v(2), def. prefix 5. xyz=w(3),(4), substitution 6. xy is a prefix of w(5), def. prefix 7. y is a suffix of xy(6), def. suffix