Question

If A = {3, 4, 5, 6} and B = {4, 6, 8, 10}, find $A\cup B$

Answer 1

Hint:The union of two sets A and B is the set of elements which are in A, in B, or in both A and B.The union of two sets A and B, written $A\cup B$, is the combination of the two sets.

Complete step-by-step answer:
The symbol used for the union of two sets is $\cup $ .
Therefore, symbolically, we write union of the two sets A and B is $A\cup B$ which means A union B.
Therefore, \[A\cup B\text{ }=\text{ }\{x\text{ }:\text{ }x\in A\text{ }or\text{ }x\in B\}\]
The given sets are
A = {3, 4, 5, 6}
B = {4, 6, 8, 10}
The union of two sets A and B is the set of elements which are in A, in B, or in both A and B.
Taking every element of both the sets A and B, without repeating any element, we get
$A\cup B=\left\{ 3,4,5,6,8,10 \right\}$

Note: The set X and set Y are the subsets of $X\cup Y$. The union of sets is commutative. The union operations are performed when the sets are expressed in roster form. The union of any set with the empty set is always the set itself.