Question

If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8} and C = {7, 8, 9, 10, 11}. Find:
(i) $A\cup B$
(ii) $A\cup C$

Answer 1

Hint:The union of 2 sets consists of all the elements present in both the sets without any repetition for $A\cup B$ , it consists of all elements of A and B without repetition. This is similar for finding $A\cup C$

Complete step-by-step answer:
The collection of elements or group of objects is called a set. Now the base operation that the set performs consists of union of sets.
We have been given A sets A, B and C separately.
A = {1,2,3,4,5}
B = {4,5,6,7,8}
C = {7, 8, 9, 10, 11}
The union of two sets A and B is equal to the set of elements which are present in set A, in set B or in both the set A and B. We can represent this operation as
$A\cup B=\left\{ a:a\in A\text{ or }a\in A \right\}$
The union of two sets A and B is defined as the set of all the elements which lie is set A and set B. We can represent it as ‘U’. We can also represent it using a Venn diagram.

                               $A\cup B$
Thus $\begin{align}
  & A\cup B=\left\{ 1,2,3,4,5 \right\}\cup \left\{ 4,5,6,7,8 \right\} \\
 & A\cup B=\left\{ 1,2,3,4,5,6,7,8 \right\} \\
\end{align}$
Similarly, $A\cup C,$ consists of all the elements that lie in set A and set C or both elements in set A and C altogether

                     $A\cup C$
$\begin{align}
  & A\cup C=\left\{ 1,2,3,4,5 \right\}\cup \left\{ 7,8,9,10,11 \right\} \\
 & A\cup C=\left\{ 1,2,3,4,5,7,8,9,10,11 \right\} \\
\end{align}$
Thus, we got,
$A\cup B=\left\{ 1,2,3,4,5,6,7,8 \right\}$ and
$A\cup C=\left\{ 1,2,3,4,5,7,8,9,10,11 \right\}$

Note: The union of two sets A and B is given by a set E, which is also a subset of the universal set U such that E consists of all those elements or members which are either in set A or set B or in both.
$A\cup B=\left\{ x:x\in A\text{ or }x\in B \right\}$