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Is the set of even integers closed under multiplication?
Yes
ARe odd integers not closed under addition?
That is correct, the set is not closed.
What does it mean to say that integers are closed under addition?
Any time you add integers, the sum will be another integer.
Are rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
Why the set of odd integers under addition is not a group?
Because the set is not closed under addition. If x and y are odd, then x + y is not odd.
Is the set of even integers closed under addition and multiplication?
Yes.
What is the set of whole numbers closed by?
If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.
Are negative integers closed under multiplication?
No.
What does it mean if an integer is closed?
You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).
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!
What is the rule of addition of integers?
negetive integers are not closed under addition but positive integers are.
Is the set of even integers closed under multiplication?
Yes
Is set of integers is a field?
The set of integers is not closed under multiplication and so is not a field.
Are integers closed under addition?
yes
Is the set of all integers closed under the operation of multiplication?
Yes.
