Write the set $\left\{\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}\right\}$ in the set-builder form.
Write the set $\left\{\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}\right\}$ in the set-builder form.
We see that each member in the given set has the numerator one less than the denominator. Also, the numerator begin from $1$ and do not exceed $6 .$ Hence, in the set-builder form the given set is
$\left\{ {x:x = \frac{n}{{n + 1}},} \right.$ where $n$ is a natural number and $\left. {1 \le n \le 6} \right\}$
Similar Questions
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{ \{ 3,4\} \} \subset A$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{ \{ 3,4\} \} \subset A$
Write the following sets in roster form :
$C = \{ x:x{\rm{ }}$ is a two-digit natural number such that sum of its digits is $8\} $
Write the following sets in roster form :
$C = \{ x:x{\rm{ }}$ is a two-digit natural number such that sum of its digits is $8\} $
Write the following intervals in set-builder form :
$\left[ { - 23,5} \right)$
Write the following intervals in set-builder form :
$\left[ { - 23,5} \right)$
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 $A \not\subset C$
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 $A \not\subset C$
List all the elements of the following sers :
$A = \{ x:x$ is an odd natural number $\} $
List all the elements of the following sers :
$A = \{ x:x$ is an odd natural number $\} $