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
$2$
$4$
$8$
$12$
Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$1 \in A$
Examine whether the following statements are true or false :
$\{ a\} \in \{ a,b,c\} $
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\varnothing \in A$
Let $A=\{a, e, i, o, u\}$ and $B=\{a, b, c, d\} .$ Is $A$ a subset of $B ?$ No. (Why?). Is $B$ a subset of $A ?$ No. (Why?)