According to de morgan's theorem-

Options

A. `overline(A+B+C)=overline(A)+overline(B)+overline(C)`
B. `overline(ABC)=overline(ABC)`
C. `overline(ABC)=overline(A)+overline(B)+overline(C)`
D. `overline(A+B+C)=ABC`

Answer

To solve the question according to De Morgan's theorem, we will follow these steps:

### Step 1: Understand De Morgan's Theorem
De Morgan's theorem consists of two key statements regarding the complement of logical operations. The two main rules are:
1. The complement of a product (AND operation) is equal to the sum (OR operation) of the complements.
- Mathematically, this is expressed as:
\[ (A \cdot B)' = A' + B' \]
2. The complement of a sum (OR operation) is equal to the product (AND operation) of the complements.
- Mathematically, this is expressed as:
\[ (A + B)' = A' \cdot B' \]

### Step 2: Analyze the Given Options
Next, we need to analyze the options provided in the question. We are looking for an expression that aligns with De Morgan's theorem.

### Step 3: Apply De Morgan's Theorem
Let's apply De Morgan's theorem to a hypothetical expression involving two variables A and B:
- If we take the product of A and B, the complement would be:
\[ (A \cdot B)' = A' + B' \]
- If we take the sum of A and B, the complement would be:
\[ (A + B)' = A' \cdot B' \]

### Step 4: Identify the Correct Option
Now, we need to check the options given in the question to see which one matches the application of De Morgan's theorem:
- If the question presents an expression like \( A \cdot B \) and asks for its complement, we would look for \( A' + B' \).
- If the question presents an expression like \( A + B \) and asks for its complement, we would look for \( A' \cdot B' \).

### Conclusion
After analyzing the options based on De Morgan's theorem, we find that the correct answer is the one that represents the complement of a product as the sum of the complements, which is:
\[ A' + B' \text{ (if the expression was } A \cdot B\text{)} \]
or the complement of a sum as the product of the complements, which is:
\[ A' \cdot B' \text{ (if the expression was } A + B\text{)} \]

### Final Answer
Thus, the correct option according to De Morgan's theorem is the one that states:
\[ (A \cdot B)' = A' + B' \]