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Prove the following Boolean relations: ...

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

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`LHD = bar(A)BC + A bar(B)C + AB bar( C) + ABC `
=` bar(A)BC + Abar(B)C + ABbar(C) + (ABC + ABC +ABC) `
[`because A + A + A = A `]
`=(bar(A)BC + ABC) + (A bar(B)C + ABC) + (AB bar( C)+ ABC)`
`= (bar(A) + A) BC + A(bar(B) + B)C + AB(bar( C) +C)`
`= 1. BC + A.1 . C + AB .1`
` = BC + AC + AB + BC + CA = RHS `
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