Chapter P.CT, Problem 1CT

To determine

To find:

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

Answer to Problem 1CT

Solution:

$(A\cup B)\cap C=\left\{2,3,5\right\}$

Explanation of Solution

Calculation:

Given,

$\begin{array}{l}A=\left\{1,2,3,4,5\right\}\\ B=\left\{2,4,6,8,10\right\}\\ C=\left\{2,3,5,7,11\right\}\end{array}$

$A\cup B=\left\{1,2,3,4,5\right\}\cup \left\{2,4,6,8,10\right\}$

Combine all the elements of the two sets with no relation of elements.

$A\cup B=\left\{1,2,3,4,5,6,8,10\right\}$

Now, $(A\cup B)\cap C.$

$(A\cup B)\cap C=\left\{1,2,3,4,5,6,8,10\right\}\cap \left\{2,3,5,7,11\right\}$

Write only the common elements of the two sets.

$(A\cup B)\cap C=\left\{2,3,5\right\}$

Final statement:

Therefore, for the given sets $A$, $B$, and $C$,

$(A\cup B)\cap C=\left\{2,3,5\right\}$