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Is the set of all integers closed under the operation of multiplication?
Yes.
What is an counterexample of the set of negative integers is closed under the operation of taking the absolute value?
-3 is a negative integer. The absolute value of -3 is +3 which is not a negative integer. So the set is not closed.
Which set is closed under the given operation 1 integers under division 2 negative integers under subtraction 3 odd integers under multiplication?
1 No. 2 No. 3 Yes.
Is set of integers is a field?
The set of integers is not closed under multiplication and so is not a field.
Is the set of integers closed under multiplication?
Yes!
Under which operation is the set of odd integers closed?
addition
Is the set of all negative integers closed for operation of addition?
yes
Is the set of all integers closed under the operation of multiplication?
Yes.
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).
What are examples of the law of closure in Mathematics?
There is no law of closure. Closure is a property that some sets have with respect to a binary operation. For example, consider the set of even integers and the operation of addition. If you take any two members of the set (that is any two even integers), then their sum is also an even integer. This implies that the set of even integers is closed with respect to addition. But the set of odd integers is not closed with respect to addition since the sum of two odd integers is not odd. Neither set is closed with respect to division.
Are integers closed under division?
No. Integers are not closed under division because they consist of negative and positive whole numbers. NO FRACTIONS!No.For a set to be closed under an operation, the result of the operation on any members of the set must be a member of the set.When the integer one (1) is divided by the integer four (4) the result is not an integer (1/4 = 0.25) and so not member of the set; thus integers are not closed under division.
Which sets of numbers are closed under subtraction?
To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.
What is an counterexample of the set of negative integers is closed under the operation of taking the absolute value?
-3 is a negative integer. The absolute value of -3 is +3 which is not a negative integer. So the set is not closed.
Which set is closed under the given operation 1 integers under division 2 negative integers under subtraction 3 odd integers under multiplication?
1 No. 2 No. 3 Yes.
Is set of integers is a field?
The set of integers is not closed under multiplication and so is not a field.
Is the collection of integers closed under subraction?
Yes, the set of integers is closed under subtraction.
ARe odd integers not closed under addition?
That is correct, the set is not closed.
