Question

Let U = {s, t, u, v, w, x, y} and A = {t, u, w, x}. Use the listing method to write the set A. A = {t, u, w, x} (Use a comma to separate answers as needed.)

Answer 1

Set
`\(A\)` is formed by extracting the common elements between the universal set
`\(U\)` and set
`\(A\)`, resulting in the elements
`\(t, u, w, x\)`. The listing method is then applied to express
`\[ A = \{t, u, w, x\} \]`.

Step-by-step explanation:

In set notation,
`\(A\)` is defined as the set containing the elements
`\(t, u, w, x\)`. To derive this set, we look for the common elements between the universal set
`\(U\)` and set
`\(A\)`. The given universal set
`\(U\)` is
`\(\{s, t, u, v, w, x, y\}\)`, and set
`\(A\)` is specified as
`\(\{t, u, w, x\}\)`. By comparing the elements of
`\(U\)` and
`\(A\)`, we identify that
`\(A\)` includes the elements
`\(t, u, w, x\)`. Therefore, the listing method representation of set
`\(A\)` is
`\(A = \{t, u, w, x\}\)`.

The listing method explicitly enumerates the elements of a set within curly braces, separated by commas. In this case,
`\(A\)` is composed of the elements
`\(t, u, w, x\)`, as specified. Each element is distinct, and the order of elements in a set does not affect its definition. Therefore, the set
`\(A\)` is accurately represented as
`\(\{t, u, w, x\}\)` using the listing method.

In summary, the final answer
`\(A = \{t, u, w, x\}\)` succinctly captures the elements of set
`\(A\)` as per the listing method, which involves listing the individual elements within curly braces.