Let's check if the expressions: $x+yz$ and $y+xz$ are equivalent or on:
$x$ | $y$ | $z$ | $yz$ | $\boldsymbol{x + yz}$ |
---|---|---|---|---|
$0$ | $0$ | $0$ | $0$ | $0$ |
$0$ | $0$ | $1$ | $0$ | $0$ |
$0$ | $1$ | $0$ | $0$ | $0$ |
$0$ | $1$ | $1$ | $1$ | $1$ |
$1$ | $0$ | $0$ | $0$ | $1$ |
$1$ | $0$ | $1$ | $0$ | $1$ |
$1$ | $1$ | $0$ | $0$ | $1$ |
$1$ | $1$ | $1$ | $1$ | $1$ |
$x$ | $y$ | $z$ | $xz$ | $\boldsymbol{y + xz}$ |
---|---|---|---|---|
$0$ | $0$ | $0$ | $0$ | $0$ |
$0$ | $0$ | $1$ | $0$ | $0$ |
$0$ | $1$ | $0$ | $0$ | $1$ |
$0$ | $1$ | $1$ | $0$ | $1$ |
$1$ | $0$ | $0$ | $0$ | $0$ |
$1$ | $0$ | $1$ | $1$ | $1$ |
$1$ | $1$ | $0$ | $0$ | $1$ |
$1$ | $1$ | $1$ | $1$ | $1$ |
Because the sequence of bits that we got under the $x + yz$ column is different from the one under the $y + xz$ column, these two expressions aren't equivalent. We say: $x + yz \neq y + xz$.