Reference no: EM131636586

Question: Let A = {x, y} and let A* be the set of all strings of finite length made up of symbols from A. A function f: A* → Z is defined as follows: For s in A*, f(s) = the number of x's minus the number of y's. Is f oneto-one? Prove or disprove. Is f onto? Prove or disprove.

2. Let A = [x, y} and let A* be the set of all strings of finite length made up of symbols from A. A function f: A* → A* is defined as follows: For s in A*, f(s) is the string obtained by writing the characters of s in reverse order. Is f one-to-one? Prove or disprove. Is f onto? Prove or disprove.

3. Let A = {x, y} and let A* be the set of all strings of finite length made up of symbols from A. A function f: A* S A* is defined as follows: For s in A*, f(s) = xs (the single-character string x followed by s). Is f one-to-one? Prove or disprove. Is f onto? Prove or disprove.