Chapter A.1, Problem 14AYU

To determine

To find: $\left(A\cap B\right)\cup C$

Answer to Problem 14AYU

$\left(A\cap B\right)\cup C=\left\{1, 3, 4, 6\right\}$

Explanation of Solution

Given:

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

Calculation:

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

$\left(A\cap B\right)=\left\{4\right\}$

$\left(A\cap B\right)\cup C=\left\{4\right\}\cup \left\{1, 3, 4, 6\right\}=\left\{1, 3, 4, 6\right\}$