To convert a logic expression into conjunctive normal form (CNF), we need to follow these steps:
Use DeMorgan's laws to push negations inwards, so that they only apply to individual variables and not to entire sub-expressions.
Use the distributive property to expand any nested sub-expressions, so that all disjunctions are at the outermost level.
Use the associative property to group any conjunctions that have the same variables.
Here is the process to convert the given logic expression into CNF:
(A ^ B v C) ^ (B v ¬ C)
Using DeMorgan's laws, we can push negations inwards:
(A ^ B v C) ^ (B v C')
Using the distributive property, we can expand the nested sub-expressions:
A^B v A^C' v B v C
Using the associative property, we can group any conjunctions that have the same variables:
(A^B v B) v (A^C' v C)
So the CNF form of the given logic expression is:
(A^B v B) v (A^C' v C)
This is in the CNF form and it is a sum of products.