# A media tycoon has an idea for an all-news television network called LNN: The Logic News Network.

A media tycoon has an idea for an all-news television network called LNN: The Logic News Network. Each segment will begin with a definition of the domain of discourse and a few predicates. The day’s happenings can then be communicated concisely in logic notation. For example, a broadcast might begin as follows: THIS IS LNN. The domain of discourse is

fAlbert; Ben; Claire; David; Emilyg:

Let D(x) be a predicate that is true if x is deceitful. Let L.(x; y) be a predicate that is true if x likes y. Let G.(x; y/)be a predicate that is true if x gave gifts to y. Translate the following broadcasted logic notation into (English) statements.

(e) How could you express “Everyone except for Claire likes Emily” using just propositional connectives without using any quantifiers (8; 9)? Can you generalize to explain how any logical formula over this domain of discourse can be expressed without quantifiers? How big would the formula in the previous part be if it was expressed this way?