In: Advanced Math
Let G be a graph. For each of the following, determine if the statement is true or false. If it's true, provide a proof and if it's false, provide a counterexample.
(a) G has a cycle if and only if G has a circuit
(b) G has a closed walk if and only if G has a circuit
(c) G has an odd-lengthed cycle if and only if G has an odd-lengthed circuit
(d) G has an odd-lengthed closed walk if and only if G has an odd- lengthed circuit