A set of connectives S is defined as complete if any sentence can be expressed using only those connectives in S. So, for instance, {and, or, not} is a complete set because all sentences can be expressed using and, or, and not.

In this problem, I am to show that the set S {conditional} is not complete. I am also to show that the set {biconditional} is not complete.

Simply using an counterexample showing a sentence that is achieved with {and, or, not} that cannot be achieved with {conditional} doesn't seem conclusive, since we can't exhaust the possible outcomes for the conditional statement. Any help is appreciated.