I'm currently working on the following problems, and wondering how I can express "otherwise" in predicate logic in a sentence like (d) below.
A hunted animal is called game. The definition of game is that everything that is either a big game or small game is a game. Examples of big games are moose, deer, boar and capercaillie. Examples of small games are fox, rabbit and bird. Write the following in predicate logic:
(a) Write the definition for game in predicate logic ∀x (Game(x) ↔ BigGame(x) V SmallGame(x)) (b) ”If there is a fox or rabbit, there is a small game” ∀x (fox(x) V rabbit(x) → SmallGame(x) ) (c) ”If there are both rabbit and moose, there are both small game and big game” ∀x (rabbit(x) ∧ moose(x) → SmallGame(x) ∧ BigGame(x) ) (d) ”If there are moose, deer, boar and capercaillie, there are big games, otherwise there are just small games” ∀x (moose(x) ∧ deer(x) ∧ boar(x) ∧ capercaillie(x) → BigGame(x) )