Which of the following are sets ? Justify your answer.
A team of eleven best-cricket batsmen of the world.
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.
Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:
$\{ x:x$ is an even natural mumber $\} \ldots \{ x:x$ is an integer $\} $
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 are examples of the null set
$\{ y:y$ is a point common to any two parallellines $\} $
State which of the following sets are finite or infinite :
$\{ x:x \in N$ and $x$ is odd $\} $
Write the set $\{ x:x$ is a positive integer and ${x^2} < 40\} $ in the roster form.