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3. Find the complement of the following expressions
(a) xy' + xY
(b) (AB' + C)D' + E
(c) ABC'D + CD') + A'B'(C* + D)(C + D*)

Can someone Answer this for mee


Sagot :

(a) xy' + xY:

xy' + xY = (xy')'(xY)' = (x' + y)(x' + Y') = x'x' + x'Y' + yx' + yY'

= 0 + x'Y' + 0 + yY' = x'Y' + yY'

Therefore, the complement of xy' + xY is x'Y' + yY'.

(b) (AB' + C)D' + E:

(AB' + C)D' + E = ((AB')'(C)')' + E = (A' + B + C')D' + E

= A'D' + BD' + C'D' + E

Therefore, the complement of (AB' + C)D' + E is A'D' + BD' + C'D' + E.

(c) ABC'D + CD' + A'B'(C* + D)(C + D*):

ABC'D + CD' + A'B'(C* + D)(C + D*) = (A' + B' + C + D') + (C + D) + (A + B + C*)(C* + D*)

= A' + B' + C + D' + C + D + A + B + CD + CD

= A' + B' + C + D' + A + B + CD + CD

Therefore, the complement of ABC'D + CD' + A'B'(C* + D)(C + D*) is A' + B' + C + D' + A + B + CD + CD.