Answer to Question #347982 in Discrete Mathematics for Kelly

Question

If U = {0,1,2,3,4,5,6,7,8,9}, A = {3,6,9} and B = {4,8}, find:

a. A _{intersection B}

_{b. A union B}

_{c. A complement}

_{d. B complement}

_{e. (A union B)complement}

Answer 1

a.

There is no common elements for $A = \{3,6,9\}$ and $B = \{4,8\}.$ Then

$$A\cap B=\{\}$$

b.

Take all elements from $A=\{3,6,9\}$ and add elements $4, 8$ from $B$

$$A\cup B=\{3.4,6,8,9\}$$

c.

All elements which are in $U = \{0,1,2,3,4,5,6,7,8,9\},$ but are not in $A = \{3,6,9\}$ we write in $A^C$

$$A^C=\{0,1,2,4,5,7,8\}$$

d. All elements which are in $U = \{0,1,2,3,4,5,6,7,8,9\},$ but are not in $B= \{4,8\}$ we write in $B^C$

$$B^C=\{0,1,2,3,5,6,7,9\}$$

e. All elements which are in $U = \{0,1,2,3,4,5,6,7,8,9\},$ but are not in

$A\cup B=\{3.4,6,8,9\}$ we write in $(A\cup B)^C$

$$(A\cup B)^C=\{0,1,2,5,7\}$$