Question
Download Solution PDFLet \(\mathrm{f}(\mathrm{~A}, \mathrm{~B})=\overline{\mathrm{A}}+\mathrm{B}\), Simplified expression for function f (f (x y, y), z) is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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
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