Respuesta :
Answer:
Integers, whole numbers and polynomials are sets of closed under multiplication.
Only Irrational numbers are not the sets of closed under multiplication.
Step-by-step explanation:
To find : Which of the following sets are closed under multiplication?
1. Integers
Yes, integers is a sets of closed under multiplication as if you multiply an integer by an integer, you will always get another integer.
Example - [tex]3\times 3=9[/tex] is an integer
2. Irrational numbers
No, irrationals are not closed under multiplication.
Example - [tex]\sqrt{3} \times \sqrt{3} =3[/tex] is a rational number
3. Whole numbers
Yes, whole numbers is a sets of closed under multiplication as if you multiply a whole number by a whole number, you will always get another whole number.
Example - [tex]5\times 5=25[/tex] is a whole number
4. Polynomials
Yes, polynomial is sets of closed under multiplication as if you multiply the variables' exponents are added, and the exponents in polynomials are whole numbers so the new exponents will be whole numbers.
Example - [tex](x + 1)(x^2 + 4x + 3) = x^3 + 5x^2 + 7x + 3[/tex] is a polynomial.
Closed under subtraction means if subtracts two numbers of a set then it must belong to that set.
The sets that are closed under subtraction are Integers and polynomials.
What is the closed under subtraction?
A set is closed under an operation if the performance of that operation on the member of the sets always produces a member of that set. So, under subtraction means if subtracts two numbers of a set then it must belong to that set.
Given
Integers, Irrational numbers, whole numbers, and polynomials.
To find
The closed under subtraction.
- Integers - They are closed under subtraction. If we subtract two integers then it will be integer only.
- Irrational numbers - They are not closed under subtraction. It [tex]2 + \rm \sqrt{2}[/tex] is subtracted by [tex]\rm \sqrt{2}[/tex] then [tex]\rm 2 + \sqrt{2} - \sqrt{2} = 2[/tex]not an irrational number.
- Whole numbers - They are not closed under subtraction. If 1 and 2 are the whole number then on subtraction 1 - 2= -1 which is not a whole number.
- Polynomials - They are closed under subtraction. If we subtract two polynomial then it will be polynomial only.
Thus, the sets that are closed under subtraction are Integers and polynomials.
More about the closed under subtraction link is given below.
https://brainly.com/question/6780033
