Question

write the set of reciprocals of natural numbers in set builder form​

Answer 1

Answer:

(i) { x:x is a positive even number }

(ii) { x:x is a whole number and x<20 }

(iii) { x:x is a positive integer and multiple of 3 }

(iv) { x:x is an odd natural number and x<15 }

Answer 2

Answer:

SET BUILDER FORM :shorthand used to write sets, often for sets with an infinite number of elements. It is used with common types of numbers, such as integers, real numbers, and natural numbers. This notation can also be used to express sets with an interval or an equation.

Step-by-step explanation:

$E$ is the set of reciprocals of natural numbers can be written as

$E=\{x: x is a natural numbers and x=\frac{1}{n} for n \in N\}$

$E=\{x: x \in N, x=\frac{1}{n} , n \in N\} \\ E=\{x \in N: x=\frac{1}{n} , n \in N\}$

1. In this form, a set is described by a characterizing property P(x) of its elements x. In such a case the set is described by {x : P(x) holds} or, {x | P(x) holds}, which is read as ‘the set of all x such that P(x) holds’. The symbol ‘|’ or ‘:’ is read as ‘such that’.
2. In other words, in order to describe a set, a variable x (say) (to denote each element of the set) is written inside the braces and then after putting a colon the common property P(x) possessed by each element of the set is written within the braces.