Let \(\mathrm{f}(\mathrm{~A}, \mathrm{~B})=\overline{\mathrm{A}}+\mathrm{B}\), Simplified expression for function f (f (x y, y), z) is :

Concept:

We are given a Boolean function in the nested form: \( f(f(xy, y), z) \). To simplify this, we need to understand how the function \( f \) behaves and use Boolean algebra rules.

Step 1: Assume definition of function

Let us assume \( f(a, b) = a + b \), a common definition used in Boolean simplification unless otherwise specified.

So,

\( f(xy, y) = xy + y \)

Using the identity: \( xy + y = y \) (Since \( y(x + 1) = y \))

Step 2: Substitute into outer function

Now substitute into the outer function:

\( f(y, z) = y + z \)

Hence, the simplified expression is:

\( y + z \)

Compare with Options:

• Option 1: \( \bar{x} + z \) ❌
• Option 2: \( xyz \) ❌
• Option 3: \( xy̅ + z \) ❌
• Option 4: None of the options ✅

Final Answer: ✅ None of the options