Which of the following is the empty set

- A
$\{ x:x$ is a real number and ${x^2} - 1 = 0\} $

- B
$\{ x:x$ is a real number and ${x^2} + 1 = 0\} $

- C
$\{ x:x$ is a real number and ${x^2} - 9 = 0\} $

- D
$\{ x:x$ is a real number and ${x^2} = x + 2\} $

Which of the following are sets ? Justify your answer.

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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:

$A, \ldots B$

Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?

$\varnothing \in A$

Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?

$\{ 3,4\} \in A$

In the following state whether $A=B$ or not :

$A=\{a, b, c, d\} ; B=\{d, c, b, a\}$