Given the Boolean Function  𝐺 = 𝑦 + 𝑥′𝑧 
1) Use the Boolean algebra to convert the inverse of the function into standard form SOP 

To convert the inverse of the Boolean function \( G = y + x' z \) into Standard Sum of Products (SOP) form using Boolean algebra, we proceed step by step.

### Step 1: Find the inverse of \( G \)

The inverse (or complement) of \( G \) is represented as \( G' \). The complement of \( G \) can be written as:

\[
G' = (y + x' z)'
\]

Using **De Morgan's Law**, we can distribute the negation over the terms:

\[
G' = y' \cdot (x' z)'
\]

### Step 2: Apply De Morgan's Law again

Now apply **De Morgan's Law** to the term \( (x' z)' \):

\[
(x' z)' = x'' + z' = x + z'
\]

Thus, the expression becomes:

\[
G' = y' \cdot (x + z')
\]

### Step 3: Distribute the terms to get SOP form

Now distribute \( y' \) over \( (x + z') \):

\[
G' = y' \cdot x + y' \cdot z'
\]

This is already in Sum of Products (SOP) form. The final SOP form for \( G' \) is:

\[
G' = y' x + y' z'
\]

### Final Answer:

The inverse of the function \( G = y + x' z \) in Standard SOP form is:

\[
G' = y' x + y' z'
\]

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Would you like any further explanation or details?

Here are 5 related questions to expand on this topic:
1. What are De Morgan's laws in Boolean algebra?
2. How can we simplify Boolean functions using Karnaugh maps?
3. What is the difference between SOP (Sum of Products) and POS (Product of Sums) form?
4. How do we convert a Boolean function into POS form?
5. What is the significance of Boolean algebra in digital logic design?

**Tip:** Always check your Boolean expressions after applying De Morgan's laws, as it's easy to miss negations.

Given the Boolean Function G = y + x' z, use Boolean algebra to convert the inverse of the function into standard form SOP.

Learn how to use Boolean algebra to find the inverse of the Boolean function G = y + x'z and convert it into standard Sum of Products (SOP) form. This solution involves De Morgan's Laws and distribution of terms, suitable for advanced high school or undergraduate students.

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