Prove directly:
A U (A' and B)= A U B
A U (A' and B)= A U B
=>
(A ∪ A') ∩ (A ∪ B) [de Morgan's law]
E ∩ (A ∪ B) [complement law]
A ∪ B [identity law]
A U (A' and B)= A U B
=>
(A ∪ A') ∩ (A ∪ B) [de Morgan's law]
E ∩ (A ∪ B) [complement law]
A ∪ B [identity law]