Question

b) The set of real numbers greater than 8 but less than 65

Answer 1

Answer:

Step-by-step explanation:

Let the number be x.

x is greater than 8. So,

x>8 or 8<x⋯(1)  

x is less than 65. So,

x<65⋯(2)  

The number x belongs to the set of real numbers. Therefore,

x∈R⋯(3)  

where  ∈  symbol represents 'belongs to'.

Combining conditions (1) and (2) gives:

8<x<65  

Now, we shall write the set builder form. Have a name for the set, say A. We combine conditions (1) and (2) (interval) and embed the condition (3) in it (restriction/domain).

A={x:8<x<65,x∈R}  

where, the symbol : denotes 'such that'. The above notation is read as:

“ Set of all x such that x is between 8 and 65 and x belongs to the set of real numbers.”