1.2 Calculation Rules and Normal Forms

Which law allows for changing the order of propositional variables connected with AND connectives?

Associative law

If all ∨ are replaced with addition and all ∧ with multiplication, which law in propositional logic resembles the laws of arithmetic?

Distributive law

What is the result of applying the absorption law to A⋁ (A⋀B) in propositional logic?

A

Which law states that ¬ (not) of a variable connected with an AND becomes an OR and vice versa?

De Morgan’s law Signup and view all the answers

How does the double negation law transform ¬ ¬A in propositional logic?

A Signup and view all the answers

Which law allows for expressing a sequence of propositional variables connected with OR | AND connectives more compactly?

Associative law Signup and view all the answers

What is a DNF in logic?

A disjunction of conjunctions Signup and view all the answers

What is the role of axioms in formal systems?

They are the initial set of propositions that are considered to be correct Signup and view all the answers

What does the symbol ⊢ indicate in logic?

That a formula can be derived in a given logical calculus Signup and view all the answers

What does it mean if a formal system contains a contradiction?

Every formula can be proven Signup and view all the answers

What is a CNF in logic?

A conjunction of disjunctions Signup and view all the answers

What is the purpose of the logical calculus in a formal system?

To infer or prove formulas from axioms Signup and view all the answers

What is the importance of the consistency of a formal system?

It ensures that only true formulas can be proven Signup and view all the answers

What is the role of transformation laws in formal systems?

They are used to derive new formulas from existing formulas Signup and view all the answers

What is the alternative calculus of propositional logic?

Truth tables Signup and view all the answers

What is the purpose of a proof in formal systems?

To show that a formula is true for every combination of truth values Signup and view all the answers

Which logical law allows one to resolve a negated bracket?

De Morgan's law Signup and view all the answers

What does a proposition in disjunctive normal form (DNF) represent?

A disjunction of conjunctions Signup and view all the answers

What does the idempotent law allow us to do when transforming propositions into normal forms?

Remove duplicates of a literal without changing the overall meaning Signup and view all the answers

What is the result of simplifying the proposition (A ∨ ¬A) ∧ (B ∨ ¬B)?

T ∧ T Signup and view all the answers

How can we transform arbitrary propositions into a normal form?

Using truth tables Signup and view all the answers

What does a proposition in conjunctive normal form (CNF) represent?