Prove the following Boolean relations:
`bar(A)BC+Abar(B)C+ABbar(C)+ABC=AB+BC+CA`

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

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

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

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

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

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. 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. bar(AB + BC + CA) = bar(A)bar(B) + bar(B)bar(C ) +bar(C)bar(A)

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