Find the complements of the expressions :(i) X + YZ + XZ(ii) AB(C�

1.	Find the complements of the expressions :(i) X + YZ + XZ(ii) AB(C’D + B’C)
Answer» (i) X + YZ + XZ = (X + YZ + XZ)’ = (X)’(YZ)’(XZ)’ = X’(Y’ + Z’)(X’ + Z’) (ii) AB(C’D + B’C) = (AB)’(C’D + B’C)’ = (AB)’((C’D)’ + (B’C)’) =(AB)’(CD’ + BC’) =(A’ + B’)+(C + D’)(B + C’)

Find the complements of the expressions :(i) X + YZ + XZ(ii) AB(C’D + B’C)

Answer»

(i) X + YZ + XZ

= (X + YZ + XZ)’

= (X)’(YZ)’(XZ)’

= X’(Y’ + Z’)(X’ + Z’)

(ii) AB(C’D + B’C)

= (AB)’(C’D + B’C)’

= (AB)’((C’D)’ + (B’C)’)

=(AB)’(CD’ + BC’)

=(A’ + B’)+(C + D’)(B + C’)

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Find the complements of the expressions :(i) X + YZ + XZ(ii) AB(C’D + B’C)

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