Question

A(1,3,5, 7,9}, B {0,1,2,3,4,5,6, 7,8,9} be the universal set and let A (0,2,4,6,8}, and C {2,3,5,7}. List the elements of the following sets 1.) Let U (a) An B (b) C\B (c) AU (Bnc)

Answer 1

Answer:

a) $A \cap B = A$

b) $C - B = {}$

c) $A \cup (B \cap C) = A \cup C = \left\{0,2,3,4,5,6,7,8\right\}$

Step-by-step explanation:

We have the following universal set

$B = \left\{0,1,2,3,4,5,6, 7,8,9\right\}$

We also have these following sets:

$A = \left\{0,2,4,6,8\right\}$

$B = \left\{2,3,5,7\right\}$

a) $A \cap B$

$A \cap B$ is the set of elements that belong to both A and B.

B is the universal set, so:

$A \cap B = A$

b) $C - B$

$C - B$ is the set with all elements that belong to C and do not belong to B.

B is the universal set, so:

$C - B =\left\{\right\}$

c) $A \cup (B \cap C)$

Because of parenthesis, $B \cap C$ takes precedence.

In a), I explained the $\cap$ operation.

B is the universal set, so:

$B \cap C = C$

Now we have $A \cup (B \cap C) = A \cup C$

$A \cup C$ is the set formed by the elements that belong to at least one of A or C.

So:

$A \cup (B \cap C) = A \cup C = \left\{0,2,3,4,5,6,7,8\right\}$