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Is the set of even integers closed under multiplication?
Yes
Is the set of all negative integers a group under addition?
no
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.
Which set is closed under the operation multiplication?
Any set where the result of the multiplication of any two members of the set is also a member of the set. Well known examples are: the natural numbers (ℕ), the integers (ℤ), the rational numbers (ℚ), the real numbers (ℝ) and the complex numbers (ℂ) - all closed under multiplication.
Is the set of positive integers a field under addition and multiplication?
NO. Certainly not. Additive inverse and Multiplicative inverse doesn't exist for many elements.
Is the set of all integers a group under multiplication?
No. The set does not include inverses.
Does the set of even integers form a group under the operation of multiplication?
No. The inverses do not belong to the group.
Example of group is an abelian group?
The set of integers, under addition.
Is set of integers is a field?
The set of integers is not closed under multiplication and so is not a field.
Are any of these sets closed under multiplication?
To determine if a set is closed under multiplication, we need to check if the product of any two elements from the set is also an element of the same set. For example, the set of integers is closed under multiplication because the product of any two integers is always an integer. In contrast, the set of natural numbers is also closed under multiplication, while the set of rational numbers is closed under multiplication as well. However, sets like the set of positive integers and the set of even integers are also closed under multiplication.
Is the set of integers closed under multiplication?
Yes!
Is set of integers closed under multiplication?
Yes!
Is the set of even integers closed under multiplication?
Yes
How are the rules for multiplication and division integers the same?
They are not the same!The set of integers is closed under multiplication but not under division.Multiplication is commutative, division is not.Multiplication is associative, division is not.
Is the set of even integers closed under addition and multiplication?
Yes.
Is the set of negative integers closed under multiplication real numbers?
No, it is not.
Is the set of all integers closed under the operation of multiplication?
Yes.
