Final answer:
The complement of the boolean function F = AB' + CD' is achieved by applying De Morgan's Theorem, resulting in F' = A'C' + A'D + BC' + BD. None of the provided options matches the correct complement following standard boolean algebra rules.
Step-by-step explanation:
The complement of the boolean function F = AB' + CD' requires finding a function that would be true whenever F is false and vice versa. In boolean algebra, the complement of a function is analogous to the logical NOT operation applied to that function. To find the complement of F, denoted as F', we apply De Morgan's Theorem which states that the complement of a sum of variables equals the product of the complements of each variable. Applying this theorem, we can find the complement of F:
- First, take the function F = AB' + CD'.
- Apply De Morgan's Theorem to get F' = (AB')'(CD')'.
- Commute the terms inside each parenthesis: F' = (A' + B)(C' + D).
- Finally, distribute each term: F' = A'C' + A'D + BC' + BD.
However, it's important to note that none of the provided options (a) AB' + CD', (b) A' + B + C' + D', (c) A'B + C'D, or (d) A' + B' + C + D is the correct complement of F. The correct complement should be A'C' + A'D + BC' + BD, assuming typical boolean algebra rules.