Question

If A = { 1, 2, 3, 4}, B = { 4, 5, 6 }, C = { 7, 8, 9 } and D = { 10, 11, 12 }, find: $A\cap \left( B\cup C \right)$

Answer 1

Hint: First we will write the definitions of required terms like intersection and union of sets and then we will use them to find the value of $A\cap \left( B\cup C \right)$ by substituting the values of A, B and C.

Complete step by step answer:
Union: The union (denoted by $\cup $ ) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other.
Intersection: The intersection of two sets has only the elements common to both sets. If an element is in just one set it is not part of the intersection. The symbol is an upside down $\cap $ .
Let’s first find the value of $B\cup C$ ,
B = { 4, 5, 6 }, and C = { 7, 8, 9 }, now we have to take all the elements that are present in both B and C.
Therefore,
$B\cup C$ = { 4, 5, 6, 7, 8, 9}
Now we will find the value of $A\cap \left( B\cup C \right)$,
A = { 1, 2, 3, 4} and $B\cup C$ = { 4, 5, 6, 7, 8, 9}, now we have to take the common elements between these two which is 4.
Therefore,
$A\cap \left( B\cup C \right)$ = { 4}
Hence, we have found the required value by using the above definitions of union and intersection.

Note: All the definitions that we have used above should be remembered by students to avoid any mistakes while solving. Students might get confused with the sign of union and intersection so one should be careful about this. One can also solve this question by using the distributive property, by breaking $A\cap \left( B\cup C \right)$ = $\left( A\cap B \right)\cup \left( A\cap C \right)$ and then we can find the values separately.