In rule method the null set is represented by
$\{\}$
$\phi $
$\{ x:x = x\} $
$\{ x:x \ne x\} $
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\varnothing \subset A$
Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.
Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
$(i)$ $\{1,2,3,6\}$ | $(a)$ $\{ x:x$ is a prime number and a divisor $6\} $ |
$(ii)$ $\{2,3\}$ | $(b)$ $\{ x:x$ is an odd natural number less than $10\} $ |
$(iii)$ $\{ M , A , T , H , E , I , C , S \}$ | $(c)$ $\{ x:x$ is natural number and divisor of $6\} $ |
$(iv)$ $\{1,3,5,7,9\}$ | $(d)$ $\{ x:x$ a letter of the work $\mathrm{MATHEMATICS}\} $ |
Which of the following pairs of sets are equal ? Justify your answer.
$\mathrm{X} ,$ the set of letters in $“\mathrm{ALLOY}"$ and $\mathrm{B} ,$ the set of letters in $“\mathrm{LOYAL}”.$
Write down all the subsets of the following sets
$\emptyset $