MTH202 Midterm Formulas

11.

Absorption Laws:

a. A A B A , b. A A B A

Implications(Conditional)& Bi-Conditional

Implication (Conditional) →

1a. p → q ≡ ~ q → ~ p, b. p → q ≡ ~ p ∨ q 2- if p → q , then its inverse is ~ p → ~ q 3- if p → q , then its converse is q → p → operator is not a commutative coz p → q ≠ q → p 4- if p → q , then its contra positive is ~ q → ~ p so p → q ≡ ~ q → ~ p, so implication is equivalent to its contra positive.

Bi-Conditional ↔

1-

p ↔ q ≡ ( p → q ) ∧ ( q → p )

2-

~ p ↔ q ≡ p ↔ ~ q

1-

p ↔ q ≡ q ↔ p

2-

Implication Law: p → q ≡ ~ p ∨ q ≡ ~ ( p ∧ ~ q)

3-

Exportation Law: ( p ∧ q ) → r ≡ p → ( q → r )

4-

Equivalence: p ↔ q ≡ ( p → q ) ∧ ( q → p )

5-

Reductio ad absurdum: p → q ≡ ( p ∧ ~ q) → c