Write the following sets in roster form :

$C = \{ x:x{\rm{ }}$ is a two-digit natural number such that sum of its digits is $8\} $

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$C = \{ x:x{\rm{ }}$ is a two-digit natural number such that the sumof its digits is $8\} $

The elements of this set are $17,26,35,44,53,62,71$ and $80$ only.

Therefore, this set can be written in roster form as $C=\{17,26,35,44,53,62,71,80\}$

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$\{1,2,3, \ldots 99,100\}$

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  • [KVPY 2013]

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\,\} $

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:

$\phi \,....\,B$