The number of elements in the set $\{ (a,\,b):2{a^2} + 3{b^2} = 35,\;a,\,b \in Z\} $, where $Z$ is the set of all integers, is
$2$
$4$
$8$
$12$
Examine whether the following statements are true or false :
$\{ 1,2,3\} \subset \{ 1,3,5\} $
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{ \{ 3,4\} \} \subset A$
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 $B = C$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{\varnothing\} \subset A$
Which set is the subset of all given sets