Math 2534 Logic Algebra Problems:
Using Logic Algebra, Prove the Following identities:
1) (P∧Q) ∨ (∼P∧Q) ∨ (∼P∧∼Q) ≡ QP∨∼
2) (P∧Q∧R) ∨ ( P∧∼Q∧R) ∨ (P∧∼Q∧∼R) ≡()PR Q
∧
∨∼
3) [(∼P∨Q) ∧ (P∨∼R)] ∧ (∼P∨∼Q) ≡PR
∧
∼∼
4) (R∨P) ∧ [(∼R∨ (P∧Q) ) ∧ (R∨Q)] ≡PQ
∧
5) ∼[(∼P∧Q) ∨ (∼P∧∼Q)] ∨ (P∧Q) ≡ P
Use Algebra of Logic to verify that the following is a tautology
6) [ P∧ (P→ Q) ∧(∼Q∨R)] → R ≡ T
Express the following expression in terms of the Nand operator.
7) P∧ (∼ Q∨R)
Simplify each statement below:
8) P→(Q →R)
9) (P∧ (Q→ R)) ∨ (∼Q ∧P)
Negate each statement and simplify
10) P→(Q →R)
11) (P∧ (Q→ R)) ∨ (∼Q ∧P)