Using correct mathematical notation and symbols, express the following in set-builder notation:
Z = {16, 17, 18, 19, 20}
{x | 15 < x < 20, x ∈ N}
see your previous post about this.
{x | 16 ≤ x ≤ 20, x ∈ z} ??
To express the set Z = {16, 17, 18, 19, 20} in set-builder notation, we write:
Z = {x | x ∈ Z, 15 < x < 21}
Explanation:
In this notation, we start with the variable x, followed by a vertical bar "|", which means "such that." After the vertical bar, we specify the conditions that x must satisfy to be included in the set.
In this case, we want to include numbers from 16 to 20, so we set the condition as 15 < x < 21. The symbol "∈" represents "belongs to" or "is an element of," and the symbol "Z" represents the set of integers.
Therefore, we specify that x belongs to the set of integers (x ∈ Z) and that x must be greater than 15 and less than 21 (15 < x < 21).
Note: It is usually common to use Z to represent the set of integers. However, if you specifically meant the set of natural numbers (N), the notation would be:
Z = {x | x ∈ N, 15 < x < 21}