Which of the following are sets ? Justify your answer.

A team of eleven best-cricket batsmen of the world.

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A team of eleven best cricket batsmen of the world is not a well-defined collection because the criteria for determining a batsman's talent may vary from person to person.

Hence, this collection is not a set.

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Which of the following are examples of the null set

Set of even prime numbers

Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?

  • [KVPY 2012]

State which of the following sets are finite or infinite :

$\{ x:x \in N$ and $2x - 1 = 0\} $

Write the following as intervals :

$\{ x:x \in R,0\, \le \,x\, < \,7\} $

If a set $A$ has $n$ elements, then the total number of subsets of $A$ is