Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.
no
no
The whole numbers are not closed under division! The statement is false since, for example, 2/3 is not a whole number.
No, it is not. Division by zero (a rational) is not defined.
division
+,-,X only
Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.
They are closed under all except that division by zero is not defined.
It means that you can do any of those operations, and again get a number from the set - in this case, a polynomial. Note that if you divide a polynomial by another polynomial, you will NOT always get a polynomial, so the set of polynomials is not closed under division.
No, they are not.
No.
no
no
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
Yes, because there is no way of multiplying two polynomials to get something that isn't a polynomial.
yes