Questions: Problem 6: ( 32 pts ) Use the Venn diagram to list each set in roster form. B ∪ C= C′= (B ∪ C)′= B ∪ C′=

Transcript text: Problem 6: ( 32 pts ) Use the Venn diagram to list each set in roster form. \[ \begin{array}{l} B \cup C= \\ C^{\prime}= \\ (B \cup C)^{\prime}= \\ B \cup C^{\prime}= \end{array} \]

Solution

Solution Steps

Step 1: Find B∪C

The union of B and C, denoted B∪C, is the set of all elements in B, or C, or both. From the Venn diagram, this includes the numbers within the circles representing sets B and C.

B∪C = {10, 25, 35, 45, 50, 75, 90}

Step 2: Find C′

The complement of C, denoted C′, is the set of all elements that are _not_ in C. From the Venn diagram, this includes the numbers outside the circle representing set C.

C′ = {15, 25, 55, 90, 95}

Step 3: Find (B∪C)′

The complement of B∪C, denoted (B∪C)′, is the set of all elements that are _not_ in B∪C. It includes everything _outside_ both circles B and C.

(B∪C)′= {15, 55}