Which of the following are sets ? Justify your answer.

The collection of ten most talented writers of India.

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The collection of ten most talented writer of India is not a well-defined collection because the criteria for determining a writer's talent vary from person to person.

Hence, this collection is not a set.

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Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then

Write down all the subsets of the following sets

$\{ 1,2,3\} $

For an integer $n$ let $S_n=\{n+1, n+2, \ldots \ldots, n+18\}$. Which of the following is true for all $n \geq 10$ ?

  • [KVPY 2013]

From the sets given below, select equal sets:

$A=\{2,4,8,12\}, B=\{1,2,3,4\}, C=\{4,8,12,14\}, D=\{3,1,4,2\}$

$E=\{-1,1\}, F=\{0, a\}, G=\{1,-1\}, H=\{0,1\}$

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

$\{1,2,3\}\subset A$