List all the elements of the following sers :
$C = \{ x:x$ is an integer ${\rm{; }}{x^2} \le 4\} $
$C = \{ x:x{\rm{ }}$ is an integer ${\rm{ }};{x^2} \le 4\} $
It can be seen that
${( - 1)^2} = 1\, \le \,4;{( - 2)^2} = 4\, \le \,4;{( - 3)^2} = 9\, > \,4$
$0^{2}=0 \leq 4$
$1^{2}=1 \leq 4$
$2^{2}=4 \leq 4$
$3^{2}=9>4$
$\therefore C=\{-2,-1,0,1,2\}$
Consider the sets
$\phi, A=\{1,3\}, B=\{1,5,9\}, C=\{1,3,5,7,9\}$
Insert the symbol $\subset$ or $ \not\subset $ between each of the following pair of sets:
$B \ldots \cdot C$
Which of the following are examples of the null set
Set of even prime numbers
Write the following sets in the set-builder form :
$\{ 3,6,9,12\}$
Which of the following are sets ? Justify your answer.
The collection of all the months of a year beginning with the letter $\mathrm{J}.$
Find the pairs of equal sets, if any, give reasons:
$A = \{ 0\} ,$
$B = \{ x:x\, > \,15$ and $x\, < \,5\} $
$C = \{ x:x - 5 = 0\} ,$
$D = \left\{ {x:{x^2} = 25} \right\}$
$E = \{ \,x:x$ is an integral positive root of the equation ${x^2} - 2x - 15 = 0\,\} $