Predicate operations
conjunction (logical AND):- {x ∈ X | P(x) ∧ Q(x) } = {x ∈ X | P(x) } ∩ {x ∈ X | Q(x) }
disjunction (logical OR):
- {x ∈ X | P(x) ∨ Q(x) } = {x ∈ X | P(x) } ∪ {x ∈ X | Q(x) }
negation (logical NOT):
- {x ∈ X | ⌉ (P(x)) } = {x ∈ X | P(x) }^{C }
combinations:
- {x ∈ X | ⌉ (P(x) ∧ Q(x) )} = {x ∈ X | ⌉ (P(x)) Ú Ø (Q(x))}
- {x ∈ X | ⌉ (P(x) ∨ Q(x) )} = {x ∈ X | ⌉ (P(x)) Ù Ø (Q(x))}
Notice that similarity of these combinations to:
- {A ∩ B}^{C} = A^{C} ∪ B^{C}
- {A ∪ B}^{C} = A^{C} ∩ B^{C}
Example: