digital logic

Question

simplify  A B' C' + D' C + [ ( A' + B + C)(D + C')]

Comments

~A + B + C ???

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a small mistake in the question, i have edited it now

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then answer will be '1'...

Answer 1

wow,,,, it is a tricky question

A B' C' + D' C + [ ( A' + B + C)(D + C')]

let x = A B' C' + D' C

then x'= (A'+B+C)(D+C')

ie here we got x + x'  which is equal to 1(as we know x+x'=1)

Answer 2

[ ( A' + B + C)(D + C')] = (A B' C' + D' C)' ( By deMorgan's identity of (X+Y)'=X'Y')

A B' C' + D' C + [ ( A' + B + C)(D + C')]  =A B' C' + D' C +(A B' C' + D' C)'

hence A B' C' + D' C +(A B' C' + D' C)'=1 as x+x'=1

hence it is simplified to 1