Questions: C and D are sets of real numbers defined as follows. C=z z ≥ 4 D=z z>5 Write C ∩ D and C ∪ D using interval notation. If the set is empty, write ∅. C ∩ D= C ∪ D=

C and D are sets of real numbers defined as follows. C=z z ≥ 4 D=z z>5 Write C ∩ D and C ∪ D using interval notation. If the set is empty, write ∅. C ∩ D= C ∪ D=
Transcript text: $C$ and $D$ are sets of real numbers defined as follows. \[ \begin{array}{l} C=\{z \mid z \geq 4\} \\ D=\{z \mid z>5\} \end{array} \] Write $C \cap D$ and $C \cup D$ using interval notation. If the set is empty, write $\varnothing$. \[ C \cap D= \] $\square$ \[ C \cup D= \] $\square$
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Solution

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Solution Steps

Step 1: Identify the Type of Inequality for Each Set

  • Set A is defined by the inequality >= with boundary 4, which translates to the interval [4, \infty).

  • Set B is defined by the inequality > with boundary 5, which translates to the interval (5, \infty).

Step 2: Finding the Intersection ($A \cap B$)
  • The intersection of Set A and Set B is: $ arnothing$.
Step 3: Finding the Union ($A \cup B$)
  • The union of Set A and Set B is: [4, \infty) \cup (5, \infty).

Final Answer:

  • Intersection: $ arnothing$
  • Union: [4, \infty) \cup (5, \infty)
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