Yes
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The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
Yes, it is.
Yes, it is closed. This means that if you multiply two even number, you again get a number within the set of even numbers.
Integers are the natural numbers (counting numbers: 1,2,3,etc.), and their negative counterparts, and zero. The set of Integers is closed for addition, subtraction, and multiplication, but not division. Closed means that the answer will be a part of the set. Example: 1/3 (1 divided by 3 equals one third) is not an integer, even though both 1 and 3 are integers.
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
Yes.
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
Yes, it is.
Yes.
No. The inverses do not belong to the group.
Yes, it is closed. This means that if you multiply two even number, you again get a number within the set of even numbers.
Integers are the natural numbers (counting numbers: 1,2,3,etc.), and their negative counterparts, and zero. The set of Integers is closed for addition, subtraction, and multiplication, but not division. Closed means that the answer will be a part of the set. Example: 1/3 (1 divided by 3 equals one third) is not an integer, even though both 1 and 3 are integers.
Subtraction: Yes. Division: No. 2/4 = is not an integer, let alone an even integer.
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
Yes, it is.
Yes. Multiplication of integers, of rational numbers, of real numbers, and even of complex numbers, is both commutative and associative.
Suppose m and n are integers. Then 2m+1 is an odd number and 2n is an even number.(2m + 1) * 2n = 4mn + 2n = 2*(2mn + 1). Since m and n are integers, the closure of the set of integers under multiplication and addition implies that 2mn + 1 is an integer. Thus the product is a multiple of 2: that is, it is even.