Logic 1

Question 1

Declarative sentences

Answer 1

A sentence which evaluates to true or false

Question 2

Propositional logic

Answer 2

Logical formulas created through variables and connectives.

Question 3

Truth tables

Answer 3

Evaluations of formulas for every value of the variables

Question 4

Valuation

Answer 4

A single combination of T/F values for a formula.

Question 5

Satisfability

Answer 5

At leaast one valuation for the formula is true

Question 6

Unsatisfability

Answer 6

No true valuations for the formula.

Question 7

Operator precedence

Answer 7

1) ¬
2) ∧ ∨
3) → ↔

Question 8

Semantic Equivalences (6)

Answer 8

1) ¬¬p ≡ p
2) p ∧ / ∨ r ≡ r ∧ / ∨ p
3) ¬(p ∧ r) ≡ ¬p ∨ ¬r / ¬(p ∨ r) ≡ ¬p ∧ ¬r
4) p ∧ / ∨ p ≡ p
5) (p ∧ / ∨ r) ∧ / ∨ s ≡ p ∧ / ∨ (r ∧ / ∨ s)
6) p → r ≡ ¬p ∨ r

Question 9

Associativity (2)

Answer 9

1) Conjunction, disjunction and XOR are associative

2) Implication is not associative

Question 10

Tautology

Answer 10

Every valuation of a formula is TRUE.

Question 11

Contradiction

Answer 11

Every valuation of a formula is false.