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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.
Are negative integers closed under multiplication?
No.
What operation is the set of positive rational numbers not closed?
subtraction. Let's take 1/2 and subtract 3/4 which is great than 1/2 so the answer is negative and hence not a positive rational.
Is the set of all integers closed under the operation of multiplication?
Yes.
Is the set of all negative integers closed for operation of addition?
yes
Is the set of integers closed under subtraction?
yes, because an integer is a positive or negative, rational, whole number. when you subject integers, you still get a positive or negative, rational, whole number, which means that under the closure property of real numbers, the set of integers is closed under subtraction.
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.
Why are rational numbers not like integers?
The set of rational numbers is closed under division, the set of integers is not.
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.
Are negative integers closed under multiplication?
No.
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.
Under which operation is the set of odd integers closed?
addition
Are rational numbers closed under subtraction operation?
Yes, they are.
How can closure property help understand the type of solution you might expect with operations?
In a group with closure the solution to the operation must be a number from the same set. The set of integers and the set of rational numbers are closed under addition. So the sum of two (or more) integers must be an integer, the sum of rational numbers must be a rational number.
What operation is the set of positive rational numbers not closed?
subtraction. Let's take 1/2 and subtract 3/4 which is great than 1/2 so the answer is negative and hence not a positive rational.
