Sets \( A \) and \( H \) are defined as follows. \( \begin{array}{l}A=\{g, h, k\} \\ H=\{d, f, g\}\end{array} \) Answer each part below. Write your answer in roster form or as \( \varnothing \). (a) Find the union of \( A \) and \( H \). \( A \cup H=\square \)

To find the union of sets \( A \) and \( H \), we combine all distinct elements from both sets. Given: \[ A = \{g, h, k\} \] \[ H = \{d, f, g\} \] The union \( A \cup H \) includes every element that is in \( A \), in \( H \), or in both. We list each unique element: - From \( A \): \( g, h, k \) - From \( H \): \( d, f \) - Note that \( g \) appears in both sets but is listed only once in the union. Therefore, the union of \( A \) and \( H \) is: \[ A \cup H = \{d, f, g, h, k\} \] **Answer:** \( A \cup H = \{\,d,\ f,\ g,\ h,\ k\,\} \)