Question

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

Answer 1

The set of all positive proper fractions with a denominator of 7 is
`\text S=[(1)/(7),\ (2)/(7),\ (3)/(7),\ (4)/(7),\ (5)/(7),\ (6)/(7)]`.

Explanation:

A proper fraction is of the form
`(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=[(1)/(7),\ (2)/(7),\ (3)/(7),\ (4)/(7),\ (5)/(7),\ (6)/(7)]`

Thus, the set of all positive proper fractions with a denominator of 7 is
`\text S=[(1)/(7),\ (2)/(7),\ (3)/(7),\ (4)/(7),\ (5)/(7),\ (6)/(7)]`.