0
Yes, it is.
Consider any two elements of this set, both are multiples of n, so they can be written as pn and qn for some integers p and q. Multiplying them together, we obtain pqn^2, which can be factored into (pqn)n. This result is clearly a multiple of n.
Since the product of any two multiples of n is also a multiple of n, the set of all multiples of n is closed under multiplication.
What else can I help you with?
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).
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.
True or False The set of whole numbers is closed under subtraction Why?
False. The set of whole numbers is not closed under subtraction. Closure under subtraction means that when you subtract two whole numbers, the result is also a whole number. However, this is not always the case with whole numbers. For example, subtracting 5 from 3 results in -2, which is not a whole number.
Is Natural numbers are closed under multiplication?
Yes.natural numbers are closed under multiplication.It means when the operation is done with natural numbers in multiplication the sum of two numbers is always the natural number.
Is the set of whole numbers are closed under multiplication?
If you can never, by multiplying two whole numbers, get anything but another whole number back as your answer, then, YES, the set of whole numbers must be closed under multiplication.
Are positive integers closed for multipication?
No, but they are closed for multiplication.
Are the integers closed under multiplication?
Yes, the integers are closed under multiplication. This means that when you multiply any two integers together, the result is always an integer. For example, multiplying -3 and 4 yields -12, which is also an integer. Therefore, the set of integers is closed under the operation of multiplication.
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 a positive number closed for addition and for multiplication?
yes
What is a Set closed under multiplication?
A set is said to be closed under multiplication if, for any two elements ( a ) and ( b ) within that set, the product ( a \times b ) is also an element of the same set. This property ensures that multiplying any two members of the set does not produce an element outside of it. 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 positive integers is also closed under multiplication for the same reason.
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).
Is it true that square of an integer will always be an integer?
Yes, it is true that the square of an integer will always be an integer. When you multiply an integer by itself, the result is an integer, as the set of integers is closed under multiplication. For example, squaring the integers 2 and -3 yields 4 and 9, respectively, both of which are integers.
Is the set of negative integers is closed under addition?
No, the set of negative integers is not closed under addition. When you add two negative integers, the result is always a negative integer. However, if you add a negative integer and a positive integer, the result can be a positive integer, which is not in the set of negative integers. Thus, the set does not satisfy the closure property for addition.
Are cubed numbers closed under multiplication?
Yes. If you have two positive integers "a" and "b", and their corresponding cubes "a^3" and "b^3" (using "^" for "power"), then the product of the two cubes would be a^3 times b^3 = (ab)^3. Since the product of "a" and "b" is also an integer, you have the cube of an integer.
Why are all the perfect squares are rational number?
A perfect square is a square of an integer.The set of integers is closed under multiplication. That means that the product of any two integer is an integer. Therefore the square of an integer is an integer.Integers are rational numbers so the square [which is an integer] is a rational number.
What operation is the set of negative rational integers closed?
The set of negative rational integers is closed under the operations of addition and multiplication. This means that when you add or multiply any two negative rational integers, the result will also be a negative rational integer. However, it is not closed under subtraction, as subtracting a larger negative integer from a smaller one can result in a non-negative integer.
Is the set of composite number closed under multiplication?
Is { 0, 20 } closed under multiplication
