Question

identify the values in the tables that express the values of each of these boolean functions. ch 12 sec 1 ex 05 1st a) f(x,y,z) = x⎯⎯ y

Answer 1

The values of the boolean function
`\(f(x,y,z) = x\overline{y}\)` are as follows:

| x | y | z | \(f(x,y,z)\) |

|---|---|---|-------------|

| 0 | 0 | 0 | 0 |

| 0 | 0 | 1 | 0 |

| 0 | 1 | 0 | 0 |

| 0 | 1 | 1 | 0 |

| 1 | 0 | 0 | 1 |

| 1 | 0 | 1 | 0 |

| 1 | 1 | 0 | 1 |

| 1 | 1 | 1 | 0 |

Step-by-step explanation:

The boolean function
`\(f(x,y,z) = x\overline{y}\)`represents the logical AND operation between (x) and the negation of y. Using this function, we can calculate its values for different combinations of (x), (y), and (z).

Starting with the input combinations of (x), (y), and (y), we proceed with evaluating the function. The negation of (y) is determined by complementing the value of (y). For example, when (x = 0) and (y = 1), the negation of (y)
`(\(\overline{y}\))` equals 0. Therefore, \(f(0,1,z)\) equals 0 regardless of the value of (y).

Similarly, when (x = 1) and (y = 0), (f(1,0,z)) results in 1, as the negation of (y\) (\(\overline{y}\)) equals 1. For other combinations, the function is evaluated accordingly.

In summary, the table shows the output of the boolean function (f(x,y,z) = x\overline{y}) for all possible combinations of (x), (y), and (z), demonstrating the resulting values based on the logical AND operation between (x) and the negation of (y).