Mcguire Dawson
02/09/2024 · Primary 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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(a) \( X \cap Y = X \)
(b) \( X \cup Y = Y \)
(c) \( X^{\prime} \cap Y^{\prime} = Y^{\prime} \)
(d) \( X \cap Y^{\prime} = \emptyset \)
(e) \( X^{\prime} \cup Y^{\prime} = X' \)
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