Give the list of elements and write in the form with condition the following sets:
the set of natural numbers that are multiples of 3
To generate the set of natural numbers that are multiples of 3, we start with the first natural number that is a multiple of 3 and continue adding 3 to that number to get the subsequent multiples.
Here's the list of elements in the set of natural numbers that are multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
In set notation, we can represent this set as:
{ x | x is a natural number and x is divisible by 3 }
Alternatively, we can also represent it using set-builder notation:
{ 3n | n is a natural number }
So, the set of natural numbers that are multiples of 3 can be expressed as:
{ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ... } or { x | x is a natural number and x is divisible by 3 } or { 3n | n is a natural number }.