(The natural numbers consist of the numbers you count with: 1, 2, 3,4, and so on.
Write in explicit set notation the set containing the odd natural
numbers.

Step-by-step explanation:

The standard sets of numbers can be expressed in all the three forms of representation of a set i.e., statement form, roster form, set builder form.

1. N = Natural numbers

= Set of all numbers starting from 1 → Statement form

= Set of all numbers 1, 2, 3, ………..

= {1, 2, 3, …….} → Roster form

= {x :x is a counting number starting from 1} → Set builder form

Therefore, the set of natural numbers is denoted by N i.e., N = {1, 2, 3, …….}

2. W = Whole numbers

= Set containing zero and all natural numbers → Statement form

= {0, 1, 2, 3, …….} → Roster form

= {x :x is a zero and all natural numbers} → Set builder form

Therefore, the set of whole numbers is denoted by W i.e., W = {0, 1, 2, .......}

3. Z or I = Integers

= Set containing negative of natural numbers, zero and the natural numbers → Statement form

= {………, -3, -2, -1, 0, 1, 2, 3, …….} → Roster form

= {x :x is a containing negative of natural numbers, zero and the natural numbers} → Set builder form

Therefore, the set of integers is denoted by I or Z i.e., I = {...., -2, -1, 0, 1, 2, ….}

4. E = Even natural numbers.

= Set of natural numbers, which are divisible by 2 → Statement form

= {2, 4, 6, 8, ……….} → Roster form

= {x :x is a natural number, which are divisible by 2} → Set builder form

Therefore, the set of even natural numbers is denoted by E i.e., E = {2, 4, 6, 8,.......}

5. O = Odd natural numbers.

= Set of natural numbers, which are not divisible by 2 → Statement form

= {1, 3, 5, 7, 9, ……….} → Roster form

= {x :x is a natural number, which are not divisible by 2} → Set builder form

Therefore, the set of odd natural numbers is denoted by O i.e., O = {1, 3, 5, 7, 9,.......}

Therefore, almost every standard sets of numbers can be expressed in all the three methods as discussed above.