Anyone hre know the boolean simplification,i have some problem with it

my question
f=a'bc+ab'c+abc'abc
f=a'b+a'b'c'd'+abcd'

explain what is te step and which rule is apply on, thks a lot, pls help me,i m preparing my exam

What does plus mean and what does concatenation mean...I can only surmise that you are using the + symbol for "or" and the concatenation to mean "and", so for instance (also the prime to mean not):

a'bc + ab'c + abc'abc ≡ (¬a ∧ b ∧ c) ∨ (a ∧ ¬b ∧ c) ∨ (a ∧ b ∧ ¬c ∧ a ∧ b ∧ c)


Otherwise, I have no idea what you are saying (and the last clause is quite redundant as I have written it).

If the above is correct, then the last clause (in the above) is false because it has ¬c ∧ c = F, meaning you have:

(¬a ∧ b ∧ c) ∨ (a ∧ ¬b ∧ c) ∨ F = (¬a ∧ b ∧ c) ∨ (a ∧ ¬b ∧ c)

In this case you can reason through it, c must be true, and then either a is true and b is false OR b is true and a is false:

c ∧ ( (¬a ∧ b) ∨ (a ∧ ¬b) )