Let $A, B,$ and $C$ be the sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$. Show that $B = C$

State which of the following sets are finite or infinite :

$\{ x:x \in N$ and $(x - 1)(x - 2) = 0\} $

Examine whether the following statements are true or false :

$\{ x:x$ is an even natural number less than $6\} \subset \{ x:x$ is a natural mumber which divide $36\} $

Write the set $\{ x:x$ is a positive integer and ${x^2} < 40\} $ in the roster form.

Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$, then the value of $m \times n$ is

- [JEE MAIN 2020]