8. The dual of the switching function x + yz is:1) yzx 2) zyx 3)  zyx 4)  z

To find the dual of the switching function $f(x, y, z) = x + yz$, we need to apply the duality principle in Boolean algebra. The dual of a function is obtained by interchanging the AND (·) and OR (+) operations, as well as the constants 0 and 1.

Step 1: Identify the Original Function

The original function is:

$f(x, y, z) = x + yz$

Step 2: Apply Duality Principle

1. Replace $+$ with $\cdot$ (OR with AND)
2. Replace $\cdot$ with $+$ (AND with OR)

Step 3: Find the Dual

Applying the duality principle to the function:

$f^D(x, y, z) = x \cdot (y \cdot z)$

Step 4: Simplify the Expression

From the dual function, we can express it as:

$f^D(x, y, z) = xyz$

Final Answer

Thus, the dual of the switching function $x + yz$ is:

$\boxed{xyz}$

However, since your options do not list $xyz$ directly, let's express what we identified:

1. $yzx$
2. $zyx$
3. $(zyx)$
4. $(z)$

Conclusion

Considering that ordering does not matter in Boolean expressions, the dual can be listed as any permutation of the terms, leading us to see that options 1, 2, and 3 are valid representations of the dual function $xyz$. We verify that the function expression matches one of the given options, concluding that the correct choice refers back to any of those interpretations.