Question

If A and B are two sets such that \[A \subset B\] then what is \[A \cup B?\]

Answer 1

Hint: If one set is the subset of another set then their union will be the bigger set. Means we will get the set of which it is a subset.

Complete step-by-step answer:
Here in this problem we are given two sets to us as A and B.
It is also said that A is a subset of B. This denotes that all the elements that are there in A are also present in the set B.
Now, as per the definition of union of sets, we have, Union of two given sets is the smallest set which contains all the elements of both the sets.
To find the union of two given sets A and B is a set which consists of all the elements of A and all the elements of B such that no element is repeated.
The symbol for denoting union of sets is ‘\[ \cup \]’.
For Example:
Let set \[A{\text{ }} = {\text{ }}\left\{ {2,{\text{ }}4,{\text{ }}5,{\text{ }}6} \right\}\]
and set \[B{\text{ }} = {\text{ }}\left\{ {4,{\text{ }}6,{\text{ }}7,{\text{ }}8} \right\}\]
Taking every element of both the sets A and B, without repeating any element, we get a new set \[ = {\text{ }}\left\{ {2,{\text{ }}4,{\text{ }}5,{\text{ }}6,{\text{ }}7,{\text{ }}8} \right\}\]. This new set contains all the elements of set A and all the elements of set B with no repetition of elements and is named as union of set A and B.
So, as all the elements of A are there in B, we will have, \[A \cup B = B\].

Note: Note that if A is a subset of B then, B is called the super set of A.
The properties of union and intersection is defined like this,
1.Commutative properties
2.Associative properties
3.Identity property for union
4.Intersection property of the empty set
5.Distributive properties