Which of the following are sets ? Justify your answer.

The collection of all the months of a year beginning with the letter $\mathrm{J}.$

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The collection of all months of a year beginning with the letter $\mathrm{J}$ is a well-defined collection of objects because one can definitely identity a month that belongs to this collection.

Hence, this collection is a set.

Similar Questions

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If $A \subset B$ and $B \in C,$ then $A \in C$

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

$\varnothing \subset A$

Write the following intervals in set-builder form :

$\left[ { - 23,5} \right)$

Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form:

$(i)$  $\{ P,R,I,N,C,A,L\} $ $(a)$  $\{ x:x$ is a positive integer and is adivisor of $18\} $
$(ii)$  $\{ \,0\,\} $ $(b)$  $\{ x:x$ is an integer and ${x^2} - 9 = 0\} $
$(iii)$  $\{ 1,2,3,6,9,18\} $ $(c)$  $\{ x:x$ is an integer and $x + 1 = 1\} $
$(iv)$  $\{ 3, - 3\} $ $(d)$  $\{ x:x$ is aletter of the word $PRINCIPAL\} $

 

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]