Let A, B and C be three atomic propositional assertions. Let P de
| Let A, B and C be three atomic propositional assertions. Let P denote [(A ∧ B) → C] and R denote [(~A → B) ∨ (~C → A)]. P → R denote _____.
A. B → C
B. B ∧ C
C. B ∨ C
D. A V B V C
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
Formula:
X → Y ≡ ~X ∨ Y ≡ X’ + Y
AND ≡ ∧ ≡ .
OR ≡ ∨ ≡ +
Calculation:
P ≡ (A ∧ B) → C
P ≡ (A.B)’ + C ≡ (ABC’)’
R ≡ [(~A → B) ∨ (~C → A)]
R ≡ [(A + B) + (C + A)] = (A + B + C)
P → R ≡ (ABC’)’ → (A + B + C)
P → R ≡ (ABC’) + (A + B + C)
∵ C + ABC’ = C + AB
P → R ≡ A + B + C + AB
P → R ≡ A + B + C
P → R ≡ A + B + C ≡ A ∨ B ∨ C