• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

Suggested languages for you:

Americas

Europe

Q9E

Expert-verified
Found in: Page 818

### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

# What values of the Boolean variables $${\bf{x}}$$ and $${\bf{y}}$$ satisfy $${\bf{xy = x + y}}$$$$?$$

The value of x=0 and y=0 or x=1 and y=1 will solve the given equation $$xy = x + y$$.

See the step by step solution

## Step 1: Definition

The complement of an element: $${\bf{\bar 0 = 1}}$$ and $${\bf{\bar 1 = }}0$$

The Boolean sum + or $$OR$$ is 1 if either term is 1.

The Boolean product $$\cdot$$ or $$AND$$ is 1 if both terms are 1.

## Step 2: Using the Boolean product and sum

The given is $$xy = x + y$$

The function has three variables x, y and z. Each of these variables can take on the value of 0 or 1.

$$\begin{array}{*{20}{r}}x&y&{x \cdot y}&{x{\bf{ + }}y}\\0&0&0&0\\0&1&0&1\\1&0&0&1\\1&1&1&1\end{array}$$

One then notes that one obtains the same value in the last two columns of the table, if x=0 and y=1 or if x=1 and y=1.

Therefore, the value of x=0 and y=0 or x=1 and y=1 will solve the given equation $$xy = x + y$$.