1. f(x,y) = x'y' + xy' + xy

| | y' | y |
| :---- | :-: | :-: |
| x' | 1 | 0 |
| x | 1 | 1 |

2. f(x,y) = x'y' + x'y

| | y' | y |
| :---- | :-: | :-: |
| x' | 1 | 1 |
| x | 0 | 0 |

This question involves simplifying Boolean expressions and interpreting truth tables. Here's a detailed explanation of each function:

Function f(x, y) = x'y' + xy' + xy
To simplify this Boolean function, we can use Boolean algebra rules. Let's analyze the given expression:

The expression is: f ( x , y ) = x ′ y ′ + x y ′ + x y

We can factor out a common term from the second and third terms: x y ′ + x y = x ( y ′ + y )

Using the complementarity law, y ′ + y = 1 , thus: x ( y ′ + y ) = x

Substituting back, we get: f ( x , y ) = x ′ y ′ + x

This expression is in its simplified form with two terms.



Function f(x, y) = x'y' + x'y
Let's simplify this function:

The expression is: f ( x , y ) = x ′ y ′ + x ′ y

We can factor out the common factor x ′ : x ′ y ′ + x ′ y = x ′ ( y ′ + y )

Again, using the complementarity law, y ′ + y = 1 , we have: x ′ ( y ′ + y ) = x ′

Thus, the simplified form of the function is: f ( x , y ) = x ′




Both functions have been simplified based on Boolean algebra rules. These steps are commonly used in digital logic design and computer science to simplify logic circuits.

Answered by EmmaGraceJohnson | 2025-07-06