EECS20N: Signals and Systems

Predicates

  • An expression like n ≤ 5 is a predicate (in the variable n) or predicate over the set Naturals. A predicate becomes an assertion whenever a value is assigned to its variable. A value satisfies a predicate if the predicate is true at that value:
n ≤ 5 is satisfied at n = 5 but it is not satisfied at n = 7.
  • Use predicate Pred(x) to define new set NewSet from existing set Set
NewSet = {x ∈Set | Pred (x) } (*)
  • Examples
{1,2,3,4,5} = { n ∈ Naturals | n ≤ 5 }

TallStudents = { name ∈ Students | name is more than 6 feet tall}
  • A predicate over a set can involve an expression in any attribute of its elements.
  • The variable name x in (*) is not significant--replacing x by y makes no difference:
{x ∈ Set | Pred(x) } = {y ∈ Set| Pred(y) } That is why x in (*) is called a dummy variable.