# Algebra of logic — how to solve the problem?

Good afternoon. Consider the following example:
(A → (B C)) Ā C (the first C, too, with a feature on the top, couldn't find that symbol)
The main problem with " → ", I don't know how to break that down. I would be grateful if comments. Thank you.
April 3rd 20 at 18:49
April 3rd 20 at 18:51
First, the usual implication
`A → (B !C) = (A → B) (A → !C)`
it can be converted to
`(!A B)(!A !C)`
Then look for the gluing.
Thank you. Here's what I came up with:
(A -> (B !C)) !A C
((A -> B) (A -> !C)) !A C
((!A B) (!A !C)) !A C
(!A B !C) !A C
But then, no how.... - eloise.Lang commented on April 3rd 20 at 18:54
April 3rd 20 at 18:53
The first part:
(A->(B^C)) == (A->B) ^ (A->!C)
(A->B) ^ (A->!C) == !((!A|B)(A|!B)(A|C)(!A|!C))
!((!A|B)(A|!B)(A|C)(!A|!C)) == !((!A ^ A + !B ^ B)(!A ^ A + !C ^ !C))
!((!A ^ A + !B ^ B)(!A ^ A + !C ^ !C)) == !(0 * !C) == 1
Second part:
1 + !A ^ C == 1 for any A and C
You can also draw the truth table and verify - Tanner77 commented on April 3rd 20 at 18:56

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