Question

Let A = {x: x is a prime number less than 10} and B = {x: x$\in N$, x is a factor of 12}. 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. Union 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 = {x: x is a prime number less than 10} = {2, 3, 5, 7}
 B = {x: x$\in N$, x is a factor of 12} = {1, 2, 3, 4, 6, 12}
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 B and C, without repeating any element, we get
$A\cup B=\{1,2,3,4,5,6,7,12\}$

Note: You might get confused about the difference between Roster and Set builder form. In roster form, all the elements of a set are listed, the elements are being separated by commas and are enclosed within braces { }. In the set builder form, all the elements of the set must possess a single property to become the member of that set.