Fresh features from the #1 AI-enhanced learning platform.Try it free
Fresh features from the #1 AI-enhanced learning platformCrush your year with the magic of personalized studying.Try it free
Question

# The Boolean operator ⊕, called the XOR operator, is defined by 1 ⊕ 1 = 0, 1 ⊕ 0 = 1, 0 ⊕ 1 = 1, and 0 ⊕ 0 = 0. Show that x ⊕ y = y ⊕ x.

Solution

Verified
Step 1
1 of 3

DEFINITIONS

The $\textbf{complement}$ of an element: $\overline{0}=1$ and $\overline{1}=0$

The $\textbf{Boolean sum}$ + or $OR$ is 1 if either term is 1.

The $\textbf{Boolean product}$ $\cdot$ or $AND$ is 1 if both term are 1.

The $\textbf{XOR operator}$ $\oplus$ is 1 if one of the terms is 1 (but not both).

## Recommended textbook solutions #### Discrete Mathematics and Its Applications

7th EditionISBN: 9780073383095Kenneth Rosen
4,283 solutions #### Discrete Mathematics

8th EditionISBN: 9780321964687 (2 more)Richard Johnsonbaugh
4,246 solutions #### Discrete Mathematics and Its Applications

8th EditionISBN: 9781259676512Kenneth Rosen
4,397 solutions #### Discrete Mathematics with Applications

5th EditionISBN: 9781337694193Susanna S. Epp
2,641 solutions