Question

List all elements of each set: The set of all positive proper fractions with a denominator of 7

Answer 1

Answer:

The set of all positive proper fractions with a denominator of 7 is $\text S=[\frac{1}{7},\ \frac{2}{7},\ \frac{3}{7},\ \frac{4}{7},\ \frac{5}{7},\ \frac{6}{7}]$.

Step-by-step explanation:

A proper fraction is of the form $\frac{x}{y}$ where the numerator is less than the denominator, i.e. x < y.

A set is a collection of items that belong to a certain experiment. Every member of a set are known as elements.

In this case we need to form a set of all positive proper fractions with a denominator of 7.

So, it is provided that y = 7.

Then the value of x has to be positive and less than 7, i.e. 1 < x < 7.

The set is:

$\text S=[\frac{1}{7},\ \frac{2}{7},\ \frac{3}{7},\ \frac{4}{7},\ \frac{5}{7},\ \frac{6}{7}]$

Thus, the set of all positive proper fractions with a denominator of 7 is $\text S=[\frac{1}{7},\ \frac{2}{7},\ \frac{3}{7},\ \frac{4}{7},\ \frac{5}{7},\ \frac{6}{7}]$.