Which of the following is the empty set

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\} $

 

Write the following sets in the set-builder form :

${\rm{\{ 5,25,125,625\} }}$

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 $A \not\subset C$

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

$\{1,2,5\}\in A$

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

$1 \in A$