- #1
Master0fN0thing
- 4
- 0
Homework Statement
Am I doing this right? The question is...
(ab) + (a' + b') = 1
Homework Equations
(a) Commutative a · b = b · a a + b = b + a
(b) Associative (a · b) · c = a · (b · c) (a + b) + c = a + (b + c)
(c) Distributive a · (b + c) = (a · b) + (a · c) a + (b · c) = (a + b) · (a + c)
(d) Identity a · 1 = a a + 0 = 0
(e) Negation a + a' = 1 a · a' = 0
(f) Double negative (a')' = a
(g) Idempotent a · a = a a + a = a
(h) DeMorgan’s laws (a · b)' = a' + b' (a + b)' = a' · b'
(i) Universal bound a + 1 = a a · 0 = 0
(j) Absorption a · (a + b) = a a + (a · b) = a
(k) Complement of 1 and 0 1' = 0 0' = 1
The Attempt at a Solution
My Steps...
(ab) + (a' + b') = (ab + a') + b' [Associative]
= (a' + ab) + b' [Commutative]
= (a' + a)(a' + b) + b' [Distributive]
= 1(a' + b) + b' [Negation]
= (a' + b) + b' [Identity]
= a' + (b + b') [Associative]
= a' + 1 [Negation]
= 1 [Absorbtion]