Question

If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}. Then find $A\cup B\cup D.$

Answer 1

Hint: $A\cup B$ means all the elements common to set ‘A’ and set ‘B’ and the remaining elements of set A and set B both as well. Apply the definition to get $A\cup B\cup D.$You can use Venn diagram as well.

Complete step-by-step answer:
Here, we have set A, B, C, D as
A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
C = {7, 8, 9, 10, 11}
D = {10, 11, 12, 13, 14}
So, we need to determine the set $A\cup B\cup D$ .
As we know $\cup $ represents a sign of union of two sets i.e., all the elements common to both sets as well as the elements which are not common in both.
$A\cup B\cup D$ will give a set of elements common to A, B and D and remaining elements of A, B, D.
So, we can get elements of $A\cup B\cup D$ by first getting the set which represents $A\cup B$ and then further $A\cup B\cup D$.
Hence, we have set A and set B as
A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}
Now, A and B have two elements in common i.e., {4, 5} and remaining elements in A and B are {1, 2, 3, 6, 7, 8}.
Hence, $A\cup B$ can be given as
$A\cup B=\left\{ 1,2,3,4,5,6,7,8 \right\}$
Now, we can calculate $A\cup B\cup D$ by using set $A\cup B$ and set D.
So, we have
$A\cup B=\left\{ 1,2,3,4,5,6,7,8 \right\}$and D = {10, 11, 12, 13, 14}
Now, no element is common in the two sets and considering the remaining elements in the two sets, $A\cup B\cup D$ can be given as
$A\cup B\cup D=\left\{ 1,2,3,4,5,6,7,8,10,11,12,13,14 \right\}$

Note: One can miss any element while writing $A\cup B$ or $A\cup B\cup D$, so be careful with the elements given in the problem. By missing one element from any set answer will be wrong.
One can get the answer of set $A\cup B\cup D$ by representing sets A, B and D in Venn diagram form as well.