Questions: Use the Venn diagram shown below to find set A′ ∩ B′. List all the elements in set A′ ∩ B′. Use commas to separate the numbers. Set A′ ∩ B′ =

Use the Venn diagram shown below to find set A′ ∩ B′. List all the elements in set A′ ∩ B′. Use commas to separate the numbers. Set A′ ∩ B′ =
Transcript text: Use the Venn diagram shown below to find set $A^{\prime} \cap B^{\prime}$. List all the elements in set $\boldsymbol{A}^{\prime} \cap \boldsymbol{B}^{\prime}$. Use commas to separate the numbers. Set $\boldsymbol{A}^{\prime} \cap \boldsymbol{B}^{\prime}=\{$
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Solution

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Solution Steps

Step 1: Find A'

A' is the complement of A, which means it contains all elements in the universal set that are not in A. The elements in set A are 4, 5, and 6. The universal set contains 1, 2, 3, 4, 5, 6, and 7. Therefore, A' = {1, 2, 3, 7}.

Step 2: Find B'

B' is the complement of B, which means it contains all elements in the universal set that are not in B. The elements in B are 2, 4, and 5. The universal set contains 1, 2, 3, 4, 5, 6, and 7. Therefore, B' = {1, 3, 6, 7}.

Step 3: Find the intersection of A' and B'

The intersection of A' and B' (A' ∩ B') consists of all elements that are in both A' and B'. A' = {1, 2, 3, 7} and B' = {1, 3, 6, 7}. Therefore, A' ∩ B' = {1, 3, 7}.

Final Answer: The final answer is $\boxed{{1, 3, 7}}$

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