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

Let's analyze the sets \( H \) and \( L \): \[ H = \{f, g, j\} \\ L = \{g, h, j\} \] ### (a) Intersection of \( H \) and \( L \) The intersection \( H \cap L \) contains all elements that are present in both \( H \) and \( L \). - Common elements in both sets: \( g \) and \( j \). \[ H \cap L = \{g, j\} \] ### (b) Union of \( H \) and \( L \) The union \( H \cup L \) contains all elements that are present in either \( H \) or \( L \). - Elements in \( H \): \( f, g, j \) - Elements in \( L \): \( g, h, j \) - Combined without repetition: \( f, g, h, j \) \[ H \cup L = \{f, g, h, j\} \] **Final Answers:** - **(a)** \( H \cap L = \{g, j\} \) - **(b)** \( H \cup L = \{f, g, h, j\} \)