Question

U={1, 2, 3, 5, 7, 8)

Answer 1

Answer:

a) $B \cup C'=\{1,3,5,7,8\}$

b) $(B \cup C)'=\{5\}$

Problem:

U={1, 2, 3, 5, 7, 8)

B={1, 3, 7,8)

C={1,2}

Find the following sets.

Write your answer in roster form or as Ø.

(a) BUC' =  

(b) (BUC)' =

Step-by-step explanation:

a)

We will need to find $C'$.

$C'$ is the elements in the universe $U$ that aren't in $C$.

$U=\{1,2,3,5,7,8\}$

$C=\{1,2\}$

So $C'=\{3,5,7,8\}$.

$B \cup C'$

$\{1,3,7,8\} \cup\{3,5,7,8\}$

union means it is in either/or so we have:

$\{1,3,5,7,8\}$

b)

We need to find $B\cup C$ first.

$B\cup C$

$\{1,3,7,8\}\cup \{1,2\}$

$\{1,2,3,7,8\}$

So now $(B \cup C)'$ means we are going to have the elements in the universe that aren't in $B \cup C$:

$U=\{1,2,3,5,7,8\}$

$B\cup C=\{1,2,3,7,8\}$

$(B \cup C)'=\{5\}$