Prove the following boolean relations.
`bar(AB + BC + CA) = bar(A)bar(B) + bar(B)bar(C ) +bar(C)bar(A)`

Prove the following boolean relations. bar(A)B + AC + BC = bar(A)B + AC

Prove the following boolean relations. AB + Abar(B) + bar(A)bar(B) = A + bar(B)

Prove the following boolean relations. (A + B)(bar(A) + C) = bar(A)B + AC

Prove the following Boolean relations: AB+bar(B)C+CA=AB+bar(B)C

Prove the following Boolean relations: A+AB+bar(A)B= bar(bar(A)bar(B)

Prove the following Boolean relations: bar(A)+AB+bar(AB)=1

Prove the following Boolean relations: ABC+bar(A)BC+Abar(B)C+bar(A)bar(B)C+bar(A)Bbar(C)+bar(A)bar(B)bar(C)=bar(A)+C

Prove the following Boolean relations: bar(A+bar(B))+bar(bar(A)+bar(B))=B

Prove the following boolean relations. bar(bar(A)+AB+bar(AB)) = 0

Prove the following boolean relations : (A + B)(bar(A) + B)bar(B) = 0