Question

Which of the following sets are closed under multiplication? Select all that apply.

Answer 1

Integers, polynomials and whole numbers are closed under multiplication

Answer 2

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 - $3\times 3=9$ is an integer

2. Irrational numbers

No, irrationals are not closed under multiplication.

Example - $\sqrt{3} \times \sqrt{3} =3$ 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 - $5\times 5=25$ 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 - $(x + 1)(x^2 + 4x + 3) = x^3 + 5x^2 + 7x + 3$ is a polynomial.