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Let A, B and C be any three logic variab...

Let A, B and C be any three logic variables, prove the following Boolean identity.
`A.B.C+A.barB.C+A.B.barC=A.(B+C)`

Text Solution

Verified by Experts

Taking L.H.S. of the given identy, we have
`=A.B.C+barB.C+B.barC`
`=A.(B.C+barB.C+barB.C]`
`=A.[B.(C+barC) +barB.C]`
`=A.[B.(1)+barB.C]=A.[B+barB.C]`
`( :' C+barC=1)`
`=A.(B+C) ( :' B+barB.C=B+C)`
Which is the right hand side of the gives identity.
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