2DD40 summary final exam

2DD40 – MATHEMATICS 1
Summary final exam



Logic 1: proposition logic
2 truth values:
- False: 0, F
- True: 1, T


Composing statements:

¬ Not

∧ And

∨ Or

↔ Is equivalent to


Truth table with →

p q p→q
0 0 1 (!)
0 1 1 (!)
1 0 0
1 1 1

Inclusive or: one of the two or both
Exclusive or: either … or …


Tautology = statement that is true for all possible truth values



Morgan: negation of ∧

¬ (p ∧ q) ↔ (¬p ∨ ¬q)

Morgan: negation of ∨

¬ (p v q) ↔ (¬p ∧ ¬q)

Negation of →

¬ (p → q) ↔ (p ∧ ¬q)

, Conjunctive Normal Form (CNF)

Form: (…) ∧ … ∧ (…)

Between the brackets only ¬ and ∨ may appear.


Disjunctive Normal Form (DNF)
Form: (…) v … v (…)

Between the brackets only ¬ and ∧ may appear.


! See slides for step-by-step plan CNF and DNF