Question

If $A = \{ 1,2,3,4,5\} ,B = \{ 2,4,6\} ,C = \{ 3,4,6\} ,$then $(A \cup B) \cap C$is
$
  A){\text{ \{ 3,4,6\} }} \\
  {\text{B) \{ 1,2,3\} }} \\
  {\text{C) \{ 1,4,3\} }} \\
 $

Answer 1

Hint: Here, we will use the concepts of intersection and the union of the sets to get the value for the resultant set value. First of all we will find the union of the two sets and then the intersection of that value with the third set to get the required value.

Complete step by step answer:
Union between the sets are defined as the elements from both the sets, it may be in one or all the sets while intersection of the sets is given by the elements which are common in all the sets.
Given that:
 $
  A = \{ 1,2,3,4,5\} \\
  B = \{ 2,4,6\} \\
  C = \{ 3,4,6\} , \\
 $
First find $(A \cup B) = \{ 1,2,3,4,5\} \cup \{ 2,4,6\} $
Taking the union of the sets, taking all the terms which are in set A and in set B.
$(A \cup B) = \{ 1,2,3,4,5,6\} $ ….. (A)
Now, $(A \cup B) \cap C = \{ 1,2,3,4,5,6\} \cap \{ 3,4,6\} $
Here taking intersection between the two sets of the above expression in which the terms are common in both the sets
$(A \cup B) \cap C = \{ 3,4,6\} $
Therefore, $(A \cup B) \cap C = \{ 3,4,6\} $. So, option (A) is correct.

Additional Information: Set builder notation is used to be well-defined as the set by numbering the elements or stating the properties to satisfy for its members. Always know the difference and co-relation between the two types of sets.

Note:
Always remember the difference between the two operations, union and the intersection and apply it accordingly. Simply intersection means common term and the union means all the elements considering all the given sets.