ACTIVITY

1. Determine which interpretations are models of: ∀x[¬P(x) => Q(x)]

Interpretation 1 Interpretation 2 Interpretation 3 
domain of discourse: { ying, yang }
P(x) : true if x = ying, false if x = yang
Q(x) : false if x = ying, true if x = yang

domain of discourse: { a, b, c }
P(x) = true if x = a, false otherwise
Q(x) = true if x = b, false otherwise

domain of discourse: integers
P(x) = true if x positive, false otherwise
Q(x) = true if x negative, false otherwise


2. Consider formula F:    ∀x[¬P(x) => P(f(x,c))]
  1. Identify the predicates, constants and functions in formula F.
  2. Consider an interpretation in which the domain be the integers, the predicate is isEven(·), and the function is plus(·,·). Find a value for the constant that makes this interpretation a model for the formula.