Question

If B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}. Find (i) $B\cup C$ (ii) $B\cup D$.

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. 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, \[A\cup B\text{ }=\text{ }\{x\text{ }:\text{ }x\in A\text{ }or\text{ }x\in B\}\]
Now let’s draw the venn diagram to find A union B.

The given sets are
B = {4, 5, 6, 7, 8},
C = {7, 8, 9, 10, 11}
D = {10, 11, 12, 13, 14}
(i) The union of two sets B and C is the set of elements which are in both B and C.
Taking every element of both the sets B and C, without repeating any element,
we get
$B\cup C=\left\{ 4,5,6,7,8,9,10,11 \right\}$
Now let’s draw the venn diagram to find B union C.

(ii) The union of two sets B and D is the set of elements which are in both B and D.
Taking every element of both the sets B and D, without repeating any element,
we get
$B\cup D=\left\{ 4,5,6,7,8,10,11,12,13,14 \right\}$
Now let’s draw the venn diagram to find B union D.

Note: You might get confused between the union and intersection of sets. In the case of union, all the elements are included in the result, but in the case of the intersection, only the common elements are considered.