Question

If A is subset of B, then $B \cup A$ is equal to:
(A) $B \cap A$
(B) $A$
(C) $B$
(D) None of these

Answer 1

Hint: A subset is a set whose elements are all members of another set. The symbol $ \subseteq $ means “is a subset of”. Example, let two sets be:
$A = \{ 1,2,3\} $
$D = \{ 0,1,2,3,4,5\} $
Since all of the members of a set $A$ are the members of set $D$. So, $A$ is a subset of $D$ and it is written as $A \subseteq D$.
So, in this question, we are to use the concept of subsets and union of two sets to find the answer.

Complete answer:
In the question, we are given that the set A is a subset of set B, i.e., $A \subseteq B$.
In other words, we can say, all the elements of A are there in the set B.
That is, set B contains all the elements of set A.
Now, we know that union of two sets consists of all the elements of both sets.
Now, $B \cup A$ means that this set contains all the elements of both $B$ and $A$.
Now, since A is a subset of B.
B already contains every element of A.
So, the union of such two sets will give us the set B as a result.
Suppose, $A = \{ 1,2,3,4,5\} $ and $B = \{ - 1,0,1,2,3,4,5,6,7,8,9\} $
So, here set A is the subset of set B as $B$ contains all the elements of $A$.
Therefore, $B \cup A$ will give set $B$ as a result.
That is, $B \cup A = B = \{ - 1,0,1,2,3,4,5,6,7,8,9\} $
Therefore, the answer is option C.

Note:
Now, a subset may be equal to the set of whose it is a subset of or may be smaller than the set. In case of being smaller than the set, then it is called a proper set more specifically and is denoted as $ \subset $. On the other hand, the set of which is a subset is called a superset. For example, let two sets be
$A = \{ 1,2,3\} $
$D = \{ 0,1,2,3,4,5\} $
Here,$A \subseteq D$, $A$ is a subset of $D$ and $D$ is called the superset of $A$.