## Related questions with answers

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

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1 of 3DEFINITIONS

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).

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