How to minimize boolean expression?

Question

Algebra

How to minimize a given algebraic boolean expression and what theorems were used?


As a result, you should get:

Answer 1

Here it is necessary to apply de Morgan's rules (twice), bracketing, associativity and the law of exclusion of the middle.
!a!b + !ab!c + !(a + !c)
!a!b + !ab!c + !ac
!a(!b ​​+ b!c + c)
Inside brackets:
!b + b!c + c = b!c + (!b + c) = b!c + !(b!c) = 1
Only !a remains