Logic and Discrete Mathematics Exam Help
I601 Logic and Discrete Math Revision Questions
Propositions, logical operations and compound propositional statements
A proposition is a declarative sentence that is either true or false, but not both. A proposition can also be considered a result of logical operators (logical connectives, AND, OR, XOR, NAND, IF THEN, IFF). New compositions, called compound propositions are formed from existing propositions using logical operators.
Classification of compound propositions
Satisfiability
A proposition is satisfiable if truth table contains True at least once.
Tautology
A proposition is a tautology if is always true (truth table consists of value True).
Contradiction
If the truth table is always false.
Contingency
A proposition is satisfiable but not a tautology.
Logical equivalence
If two propositions, p and q, have the same value in all possible cases are called logically equivalent, p ≡ q, if p↔q.
Contrapositive
The negative version of the positive logical proposition, p∨q≡¬p∧¬q.
Converse
The mirror opposite of a logical proposition.
| p | q | p→q | q→p |
|---|---|---|---|
| T | T | T | T |
| T | F | F | T |
| F | T | T | F |
| F | F | T | T |
Algebra of propositions
Conjunctive and Disjunctive Normal Form of propositional statements
Predicates and quantifiers
Bound and free variables
Logical equivalences for quantifiers
Propositional calculus (PC)
Derivation in classical logic
Semantics of predicate calculus
Validity and satisfiability of predicate statements
Sequent predicate calculus LK
A way of deducing if a logic statement is true or not. Please see yourself to the interactive tutorial of the Sequent Calculus (LK).
