Tony, Mike, and John belong to the Alpine Club. Every member of the Alpine Club is either a skier or a mountain climber or both. No mountain climber likes rain, and all skiers like snow. Mike dislikes whatever Tony likes and likes whatever Tony dislikes. Tony dislikes rain and snow. Represent this information by predicate-calculus sentences in such a way that you can represent the question Is there a member of the alpine club who is a skier but not a mountain climber? as a predicate-calculus expression.