Question

Consider three sets A, B and C such that $A=\left\{ 1,3,5 \right\},B=\left\{ 2,4,6 \right\}$ and $C=\left\{ 0,2,4,6,8 \right\}$ then find the universal set.

Answer 1

Hint:Universal sets contain all the elements in the given set A, B and C. The elements of set A, B and C are together available in set U, which is the universal set without any repetition.

Complete step-by-step answer:
The collection of elements or group of objects is called a set. Universal set contains a group of objects or elements which are available in all the sets. A universal set contains all the elements or objects of other sets including its own elements. It can be represented by the symbol ‘U’.
Now we have been given the sets which are,
A = {1, 3, 5}
B = {2, 4, 6}
C = {0, 2, 4, 6, 8}
Thus, the universal set will be the combination of all the elements in the sets A, B and C.
Thus, universal set, \[\begin{align}
  & U=A+B+C \\
 & U=\{1,3,5\}\cup \left\{ 2,4,6 \right\}\cup \left\{ 0,2,4,6,8 \right\} \\
 & =\left\{ 1,3,5,2,4,6,0,8 \right\}
\end{align}\]
Thus, Universal set, $U=\left\{ 1,3,5,2,4,6,0,8 \right\}$
From this we can see that the elements of sets A, B and C are altogether available in the universal set ‘U’. In the universal set ‘U’ no elements are repeated and all the elements are unique.
Thus, we found the universal set as,
$U=\left\{ 0,1,2,3,4,5,6,8 \right\}$

Note: If a universal set contains sets A, B and C, then these sets are also called subsets of the universal set. This can be denoted by,
$A\subset U$ (A is a subset of U)
$B\subset U$ (B is a subset of U)
$C\subset U$ (C is a subset of U)