King Neptune has a problem. His daughter Ariel is deeply in love with the handsome prince Eric. However, King Neptune is strongly against a marriage of Ariel and Eric (as Ariel is a mermaid and Eric is a human.) He calls his royal advisor Sebastian. Now, according to the laws of the undersea kingdom, marriages are determined at a royal ball. The king must invite Ariel and Eric at the ball, but he may also invite other mermen and mermaids, but always the same number of mermen as of mermaids. The Gale- Shapley algorithm is carried out, and a stable marriage is thus formed, matching each of the mermen and Eric with a mermaid. The king and Sebastian can bribe the other participants of the ball in making their preference list in any order the king and Sebastian would want. And, they can choose in which order the Gale-Shapley algorithm is carried out. Actually, they can modify everything they want, with the following exceptions: Ariel has Eric at the top of her preference list. Eric has Ariel at the top of his preference list. The Gale-Shapley algorithm is used. . Is it possible for the king and Sebastian to arrange things such that Eric and Ariel are not matched, or is a marriage between Ariel and Eric unavoidable? Give a short proof of your answer.