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
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
