Represent the following sets in set-builder form $X = \{S u n d a y, M o n d a y, T u e s d a y, W e d n e s d a y, T h u r s d a y, F r i d a y, S a t u r d a y\}$
A $= {1, 1 / 2, 1 / 3, 1 / 4, 1 / 5, . . . . . .}$

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Solution

Step-1 : Set builder form of $X = \{S u n d a y, M o n d a y, T u e s d a y, W e d n e s d a y, T h u r s d a y, F r i d a y, S a t u r d a y\}$
$X = \{S u n d a y, M o n d a y, T u e s d a y, W e d n e s d a y, T h u r s d a y, F r i d a y, S a t u r d a y\}$
The set $X$ contains all the days of the week.
Therefore, we can write it as,
$X = {x : x i s a d a y i n a w e e k}$
Step-2 : Set builder form of $= {1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, . . . . . .}$
$A = {1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, . . . . . .}$
Now,
Set $A$ contains elements $1, 2, 3, 4, \dots . .$ in the denominator.
Therefore,
$A = {x : x = \frac{1}{n}, n \in N}$
Hence set buider forms are $X = {x : x is a day in a week}$ and $A = {x : x = \frac{1}{n}, n \in N}$

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Represent the following sets in set-builder form $X = \{S u n d a y, M o n d a y, T u e s d a y, W e d n e s d a y, T h u r s d a y, F r i d a y, S a t u r d a y\}$
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