Hammond Wilson
08/21/2024 · High School

3. Let \( X \) and \( Y \) denote two sets. If \( X \subset Y \) simplify each of the following as far as possible and where necessary, show the results in a Venn diagram. \( \begin{array}{lllll}\text { (a) } X \cap Y & \text { (b) } X \cup Y & \text { (c) } X^{\prime} \cap Y^{\prime} & \text { (d) } X \cap Y^{\prime} & \text { (d) } X^{\prime} \cup Y^{\prime}\end{array} \)

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1. \( X \cap Y = X \) 2. \( X \cup Y = Y \) 3. \( X' \cap Y' = Y' \) 4. \( X \cap Y' = \emptyset \) 5. \( X' \cup Y' = X' \)

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