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 $B = C$

Decide, among the following sets, which sets are subsets of one and another:

$A = \{ x:x \in R$ and $x$ satisfy ${x^2} – 8x + 12 = 0 \} ,$

$B=\{2,4,6\}, C=\{2,4,6,8 \ldots\}, D=\{6\}$

State which of the following sets are finite or infinite :

$\{ x:x \in N$ and $x$ is prime $\} $

Which of the following are sets ? Justify your answer.

A collection of novels written by the writer Munshi Prem Chand.

State which of the following sets are finite or infinite :

$\{ x:x \in N$ and $x$ is odd $\} $