The question asks to express the values of the Boolean functions using a truth table. I will create a truth table for each of the four Boolean functions (a, b, c, and d). Let me break down each function and solve it step-by-step.

1. Variables: We have three Boolean variables: $x$, $y$, and $z$. Each variable can take a value of 0 (false) or 1 (true).
2. Truth Table: A full truth table for 3 variables will have $2^3 = 8$ rows, covering all combinations of $x$, $y$, and $z$.

Let's calculate the output for each function and build the truth table.Here is the truth table for the given Boolean functions:

This table provides the output for each function $F(a)$, $F(b)$, $F(c)$, and $F(d)$ based on all possible values of $x$, $y$, and $z$.

Do you need further details or any clarifications?

Here are 5 additional questions to explore the topic further:

1. What are the applications of Boolean functions in digital circuits?
2. How can Boolean functions be minimized using Karnaugh maps?
3. How do De Morgan's laws apply to the functions presented in this table?
4. How would the truth table change if we had more variables?
5. Can you express these Boolean functions in terms of logic gates?

Tip: Truth tables are a key tool in simplifying Boolean expressions and are widely used in designing digital circuits.