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.
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}\} $ |
Are the following pair of sets equal ? Give reasons.
$A = \{ x:x$ is a letter in the word ${\rm{FOLLOW }}\} $
$B = \{ y:y$ is a letter in the word $WOLF\} $
Let $A, B$ and $C$ be three sets. If $A \in B$ and $B \subset C$, is it true that $A$ $\subset$ $C$ ?. If not, give an example.
Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:
$\{ x:x$ is a triangle in a plane $\} \ldots \{ x:x$ is a rectangle in the plane $\} $
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{ \{ 3,4\} \} \subset A$