Question

What does $ \cup $mean in the math domain?

Answer 1

Hint:"Domain" refers to the numbers you pass to the function. "Range" refers to the numbers returned by the function. The first distinction between domain and range is that domain is plotted on X-coordinates, whereas range is plotted on Y-coordinates. The rule applies even when you have to find the domain and range from existing graphs.

Formula Used:
Union of the sets –
$X \cup Y = \left\{ {x:x \in X or x \in Y} \right\}$
Here, $X$ and $Y$ are two sets.

Complete step by step Solution:
The union of two sets is the smallest set that contains all of the elements from both sets.
To find the union of two sets, consider X and Y, which contain all of X's elements and all of Y's elements such that no element is repeated.
$ \cup $ is the symbol for representing the union of sets.
Let, two sets are $A$ and $B$
Where, $A = \left\{ {1,3,5,7,7} \right\}$ and $B = \left\{ {2,4,6,9} \right\}$
Now while writing the union of both sets we’ll take each and every element. Also, we’ll make sure that no element will be repeated.
Therefore, $A \cup B = \left\{ {1,2,3,4,5,6,7,9} \right\}$

Note: The key concept involved in solving this problem is a good knowledge of sets. Students must know that German mathematician Georg Cantor (1845-1918) was the first to propose the basic concept of 'Set Theory.'