Write the following sets in the set-builder form :
${\rm{\{ 5,25,125,625\} }}$
Write the following sets in the set-builder form :
${\rm{\{ 5,25,125,625\} }}$
$\{ 5,25,125,625\} $
It can be seen that $5=5^{1}, 25=5^{2}, 125=5^{3},$ and $625=5^{4}$
$\therefore \{ 5,25,125,625\} = \{ x:x = {5^n},n \in N{\rm{ }}$ and ${\rm{ }}1\, \le \,n\, \le \,4\} $
Similar Questions
In rule method the null set is represented by
In rule method the null set is represented by
Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then
Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then
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\} $
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\} $ |
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 $x \in A$ and $A \in B,$ then $x \in B$
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 $x \in A$ and $A \in B,$ then $x \in B$
Write the following intervals in set-builder form :
$\left[ { - 23,5} \right)$
Write the following intervals in set-builder form :
$\left[ { - 23,5} \right)$