Question

For what values of x, y, and z, including null, does the boolean expression x ≤ 3 or not(y ≥ 1 and z = 5) have the truth value false? Identify one of those values from the list below.

Answer 1

The boolean expression is false when x > 3 and y ≥ 1 and z = 5. From the given list, x = 20 is the value that satisfies the condition for x. Without y and z values, we cannot ascertain the total truth value.

Step-by-step explanation:

The boolean expression in question is x ≤ 3 or not(y ≥ 1 and z = 5). For the entire expression to be false, both parts separated by 'or' must be false. That means x must be greater than 3, and the expression 'not(y ≥ 1 and z = 5)' must also be false. For the latter to be false, the condition within the parentheses (y ≥ 1 and z = 5) must be true.

Therefore, we are looking for values where x is greater than 3, y is greater than or equal to 1, and z is equal to 5.
From the provided list, we can interpret the following values:

• 13 z = 2.78
• 15 x = 20
• 17 x = 6.5
• 19 x = 1
• 21 x = 1.97
• 23 z = -1.67
• 25 z≈ -0.33
• 27 0.67, right
• 29 3.14, left
• 31 about 68 percent
• 33 about 4 percent
• 35 between -5 and -1

Among these values, the one that makes the original expression false is:

1. x = 20

This value clearly shows that x is greater than 3, which satisfies the first condition for the entire expression to be false. However, without the corresponding values of y and z being greater than or equal to 1 and exactly 5, respectively, we cannot definitively say that the entire expression is false. We only know this part of the expression would be false.