(A+B')' (A'+B) convert to product of sums

Question

(A+B')' (A'+B) convert this to PoS (product of sums ) expression using De Morgan's law

i can do (A+B') (A'+B) one but i can not convert (A+B')' (A'+B) because it has single over bars on more than one variable.please help me

Answer 1

(A+B')'(A'+B)    starting expression
(A'B)(A'+B)      De Morgan on (A+B')'
A'BA'+A'BB       distributive property
A'A'B+A'BB       commutative property
A'B+A'BB         XX=X on A'A'B
A'B+A'B          XX=X on A'BB
A'B              X+X=X on A'B+A'B

我不知道我称之为“sums的产品”形式，但它是最简单的等价表达式。如果你真的坚持总和的产品，那么我们可以反过来运行X+X=X规则：

A'B               starting expression
(A'+A')B          X=X+X on A'
(A'+A')(B+B)      X=X+X on B