Which of the following pairs of sets are equal ? Justify your answer.
$\mathrm{X} ,$ the set of letters in $“\mathrm{ALLOY}"$ and $\mathrm{B} ,$ the set of letters in $“\mathrm{LOYAL}”.$
We have, $X =\{ A , L , L , O , Y \}, B =\{ L , O , Y , A , L \} .$ Then $X$ and $B$ are equal sets as repetition of elements in a set do not change a set. Thus,
$X=\{A, L, O, Y\}=B$
Write the following intervals in set-builder form :
$\left( { - 3,0} \right)$
Write the following as intervals :
$\{ x:x \in R, - 12\, < \,x\, < \, - 10\} $
Which of the following are examples of the null set
Set of even prime numbers
Write down all the subsets of the following sets
$\emptyset $
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 $A \not\subset B$ and $B \not\subset C,$ then $A \not\subset C$