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The table you've shared defines four different Boolean functions \( F_1, F_2, F_3, F_4 \) based on the input \( x \), which takes binary values (0 and 1). The functions take values of either 0 or 1 depending on \( x \).

The table looks as follows:

\[
\begin{array}{c|c|c|c|c}
x & F_1 & F_2 & F_3 & F_4 \\
\hline
0 & 0 & 0 & 1 & 1 \\
1 & 0 & 1 & 0 & 1 \\
\end{array}
\]

We need to determine the degree of these Boolean functions. The degree of a Boolean function refers to the number of variables involved in the simplest form of its expression. Since this table only uses a single variable \( x \), we focus on linear or constant functions.

- \( F_1(x) \): The output is \( F_1 = 0 \) for both values of \( x \). This is a constant function with degree 0.
- \( F_2(x) \): The output changes from 0 to 1 as \( x \) goes from 0 to 1. This is a linear function, and its degree is 1.
- \( F_3(x) \): The output changes from 1 to 0 as \( x \) goes from 0 to 1. This is also a linear function, with degree 1.
- \( F_4(x) \): The output is \( F_4 = 1 \) for both values of \( x \), making it a constant function with degree 0.

Thus, we have:

- Two constant functions \( F_1 \) and \( F_4 \) (degree 0).
- Two linear functions \( F_2 \) and \( F_3 \) (degree 1).

The highest degree among these is 1, so the correct answer is **1**.

Would you like more details or have any questions? Here are 5 related questions:

1. How do you express a Boolean function in canonical form?
2. Can Boolean functions have a degree higher than 1 for more variables?
3. What are the applications of Boolean functions in digital circuits?
4. How are linear and constant Boolean functions used in computing?
5. What is the significance of the degree of a Boolean function in simplification?

**Tip**: Boolean functions are essential in the design of digital logic circuits, where their degree helps define the circuit's complexity.

There are four different Boolean functions F1, F2, F3, and F4 for degree based on the given table.

This problem determines the degree of four Boolean functions F1, F2, F3, and F4 from a given table. Concepts include constant and linear Boolean functions, suitable for students studying Boolean algebra at the undergraduate level.

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