Yes, they are.
Subtraction.
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
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.
Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.
Not by itself. A mathematical operation has properties in the context of a set over which it is defined. It is possible to have a set over which properties are not valid.Having said that, the set of rational numbers is closed under subtraction, as is the set of real numbers or complex numbers.Multiplication is distributive over subtraction.
Yes. The rational numbers are a closed set with respect to subtraction.
Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.
The set of rational numbers is closed under all 4 basic operations.
The set of integers, rational numbers, real numbers, complex numbers are some of the sets. Also, many of their subsets: for example, all numbers divisible by 3.
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.
Because when one rational number is subtracted from another rational number the result is a rational number. Don't forget that integers (ℤ) are a subset of rational numbers (ℚ).
If a set is closed under an operation. then the answer will be a part of that set. If you add, subtract or multiply any two rational numbers you get another national number. But when it comes to division, it is closed except for one number and that is ZERO. eg 3.56 (rational number) ÷ 0 = no answer. Since no answer is not a rational number, that rational numbers are not closed under the operation of division.