EECS20N: Signals and Systems

• Home
• What are sets?
• Variables
• Assertion
• Some basic sets
• Functions
• Predicates
• More sets
• Set operations
• Product sets
• Syntax
• Predicates
• Parsing
• Truth
• Product sets

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:

{x∈ Reals | (x > 5) ∧ ⌉ (x ≥ 7)} = (5, 7)