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Is the set of all even integers closed with respect to addition?
Yes, it is.
Is the set of all integers closed under the operation of multiplication?
Yes.
What binary operations have closure?
Closure depends on the set as much as it depends on the operation.For example, subtraction is closed for all integers but not for natural numbers. Division by a non-zero number is closed for the rational numbers but not integers.The set {1, 2, 3} is not closed under addition.
Which set of numbers is closed under addition?
Natural (ℕ), integer (ℤ), rational (ℚ), real (ℝ) and complex (ℂ) numbers are all closed under addition.
What are the properties of number?
Different sets of numbers have different properties. For example,The set of counting numbers is closed under addition but not under subtraction.The set of integers is closed under addition, subtraction and multiplication but not under division.Rational numbers are closed under all four basic operations of arithmetic, but not for square roots.A set S is "closed" with respect to operation # if whenever x and y are any two elements of S, then x#y is also in S. y = 0 is excluded for division.So, the answer depends on what you mean by "number".
Is the set of all negative integers closed for operation of addition?
yes
Is the set of all even integers closed with respect to addition?
Yes, it is.
Is the set of all negative integers a group under addition?
no
Is the set of all integers closed under the operation of multiplication?
Yes.
What binary operations have closure?
Closure depends on the set as much as it depends on the operation.For example, subtraction is closed for all integers but not for natural numbers. Division by a non-zero number is closed for the rational numbers but not integers.The set {1, 2, 3} is not closed under addition.
Are rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
Which set of numbers is closed under addition?
Natural (ℕ), integer (ℤ), rational (ℚ), real (ℝ) and complex (ℂ) numbers are all closed under addition.
Give two reason for the set of odd integers is not a group?
Assuming that the question is in the context of the operation "addition", The set of odd numbers is not closed under addition. That is to say, if x and y are members of the set (x and y are odd) then x+y not odd and so not a member of the set. There is no identity element in the group such that x+i = i+x = x for all x in the group. The identity element under addition of integers is zero which is not a member of the set of odd numbers.
What are the properties of number?
Different sets of numbers have different properties. For example,The set of counting numbers is closed under addition but not under subtraction.The set of integers is closed under addition, subtraction and multiplication but not under division.Rational numbers are closed under all four basic operations of arithmetic, but not for square roots.A set S is "closed" with respect to operation # if whenever x and y are any two elements of S, then x#y is also in S. y = 0 is excluded for division.So, the answer depends on what you mean by "number".
Why is a set of positive integers not a group under the operation of addition?
The set of positive integers does not contain the additive inverses of all but the identity. It is, therefore, not a group.
How are Integers combined?
All numbers - integers as well as non-integers - are combined using different mathematical operations. Some operators are binary: that is, they combine two numbers to produce a third; some are ternary (combine 3 to produce a fourth) and so on.The set of integers is closed under some operations: common examples are addition, subtraction, multiplication, exponentiation. But not all operators are: division, for example.
Are rational numbers are closed under addition subtraction division or multiplication?
The set of rational numbers is closed under all 4 basic operations.
