Question

Consider any two sets A and B such the $A\subset B$ then find \[A\cup B\]

Answer 1

Hint:$A\subset B$ means A is a subset of B and all the elements of A are in B. Thus, take up examples of set A and B, where A is a subset of B and find the value of $A\cup B$

Complete step-by-step answer:
We have been given two sets A and B. A subset is a set where elements are all members of another set. The symbol $''\subset ''$ in $A\subset B$ means that A is a proper subset of B which means that all the elements of A are in B but B contains at least one element that is not in A.
This can be explained by taking a few examples. Let us consider
$A=\{1,2\}$ and $B=\{1,2,3\}$
Now every elements of A is there in B. Thus, A is a subset of B i.e. $A\subset B$
Hence $A\cup B=\{1,2\}\cup \{1,2,3\}$
Now, $A\cup B=\{1,2,3\}$
From this we can say that $A\cup B=B$ i.e B = {1, 2, 3}
Let us look into one more example where,
A = {1, 2, 3} B = {0, 1, 2, 3, 4, 5}
\[\begin{align}
  & \therefore A\cup B=\{1,2,3\}\cup \{0,1,2,3,4,5\} \\
 & \text{ }=\{0,1,2,3,4,5\} \\
\end{align}\]
Thus $A\cup B=B$
Thus, for two sets A and B, when $A\subset B,$ the value of, $A\cup B=B$
$\therefore A\cup B=B$

Note: If we were given $B\subset A$ , then B is the proper subset of A. Thus, all the elements of B are in A but A contains at least one element that is not in A. Thus when $B\subset A,$
$A\cup B=A$