Question

If $A=\left\{ 4,5,6 \right\}$ ; $B=\left\{ 7,8 \right\}$ then show that $A\cup B=B\cup A$

Answer 1

Hint: Here we have been given two sets $A$ and $B$ and we have to show that $A\cup B=B\cup A$. Now as we know, the union of two sets is equal to all the terms inside the sets given. Which means the union of $A$ and $B$ is equal to all the terms in both of them. Finally we will check whether the two values obtained are the same or not and get our desired answer.

Complete step by step answer:
The two sets are given as follows:
$A=\left\{ 4,5,6 \right\}$
$B=\left\{ 7,8 \right\}$
We have to show that,
$A\cup B=B\cup A$
According to logic of union of sets, we can find
$A\cup B=\left\{ 4,5,6,7,8 \right\}$
Next we will find the value of the right side as follows,
$B\cup A=\left\{ 7,8,4,5,6 \right\}$
As both the sets contain same elements irrespective of the order
Therefore, $A\cup B=B\cup A$
Hence proved.

Note:
It doesn’t matter what is the order of the element in the set, if two sets contain the same number of elements they are said to be equal irrespective of the order of the elements in the sets. Main confusion that usually occurs is between universal set and union set. Where the union set is the union of two or more sets resulting in the collection of all the elements present in the two sets whereas the universal set is itself a set from which all other sets are derived. Union sets satisfy many laws such as commutative law, Associative law, Identity law, Idempotent law and domination law.