Dnf to rmnf

Question

I found the dnf is !a&!b or !c . I tried to convert into rmnf. But i am getting wrong answer when I check with the tool. Can you write the rmnf with steps.

Answer 1

Here is a step by step computation:

    !a&!b|!c
        = !a&!b&c|!c
        = !a&!b&c⊕!c
        = (a⊕true)&(b⊕true)&c ⊕ (c⊕true)
        = (a⊕true)&(b⊕true)&c ⊕ c ⊕ true
        = (a&b ⊕ a ⊕ b ⊕ true)&c ⊕ c ⊕ true
        = (a&b&c ⊕ a&c ⊕ b&c ⊕ c) ⊕ c ⊕ true
        = a&b&c ⊕ a&c ⊕ b&c ⊕ c ⊕ c ⊕ true
        = a&b&c ⊕ a&c ⊕ b&c ⊕ true