Question - Complement of a Logical Function

The complement of the function \( F(A,B,C,D) = (AB+C)(B'+C)(CD+C') \) is found by applying De Morgan's laws.

Using De Morgan's laws to find the complement, we get:

\( F'(A,B,C,D) = (AB+C)' + (B'+C)' + (CD+C')' \)

\( F'(A,B,C,D) = (A'+B')(B+C')(C'+D)(C) \)

Now by applying the Absorption law \( X + X'Y = X + Y \) we can simplify:

\( F'(A,B,C,D) = A' + B'C' + C'D + C \)

Further simplifications can be done by absorbing \( C \) into \( B'C' \) and \( C'D \), because \( C \) alone makes the combined expression true regardless of other terms:

\( F'(A,B,C,D) = A' + C \)

To match the form given in the multiple-choice options, we can express it using 'or' (addition) for each variable:

\( F'(A,B,C,D) = A'B'C'D' + A'B'C'D + A'B'CD' + A'B'CD + AB'C'D' + AB'C'D + AB'CD' + AB'CD \)

This full expression covers all possibilities for the complement. However, given the options are not of this form, we recognize that no further simplification would result into one of the given options. Therefore, the original simplification \( F'(A,B,C,D) = A' + C \) indicates there might be a mistake either in the options provided or in the way the question is understood.