For an integer $n$ let $S_n=\{n+1, n+2, \ldots \ldots, n+18\}$. Which of the following is true for all $n \geq 10$ ?
$S_n$ has a multiple of $19$
$S_n$ has a prime
$S_n$ has at least four multiples of $5$
$S_n$ has at most six primes
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\} $
Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:
$\{ x:x$ is a student of class $\mathrm{XI}$ of your school $\} \ldots \{ x:x$ student of your school $\} $
Write the following sets in the set-builder form :
$\{ 3,6,9,12\}$
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
Write the following intervals in set-builder form :
$\left( {6,12} \right]$