# Exchange Operation as Replacement Operations

## Example of use of Replacement Operation

Let $x$ and $y$ be variables whose values are to be exchanged.

The exchange operation on $x$ and $y$ can be implemented using replacement operations.

Let $t$ be a third variable which has been established for this purpose.

Then the sequence of replacement operations:

$t \gets x$
$x \gets y$
$y \gets t$

## Proof

Observing the values of the variables after each replacement operation:

Operation $x$ $y$ $t$
$t \gets x$ $x$ $y$ $x$
$x \gets y$ $y$ $y$ $x$
$y \gets t$ $y$ $x$ $x$

Hence the result.

$\blacksquare$