Yes.
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.
No. The product of two primes cannot, by definition, be a prime.
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.
No.
No.
Is { 0, 20 } closed under multiplication
Because it is a product of real numbers. And the set of real numbers is closed under multiplication.
A set is closed under multiplication if for any two elements, x and y, in the set, their product, x*y, is also a member of the set.
No. The product of two primes cannot, by definition, be a prime.
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.
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.
Rational numbers are closed under multiplication, because if you multiply any rational number you will get a pattern. Rational numbers also have a pattern or terminatge, which is good to keep in mind.
No.
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.
No.
No.
No.