Question

prove that rational numbers are closed or not closed under addition​

Answer 1

Step-by-step explanation:

So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number. Rationals are closed under addition (subtraction).

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Answer 2

Answer:

Yes, rational numbers are closed under addition according to different properties.

Step-by-step explanation:

The properties are:-

# Closure property

The sum of two rational numbers is a rational number.

Adding two rational numbers will result in another rational number. Thus, adding two rational numbers produces another rational number.

Let's take p/q, r/s and t/u as an example;

p/q + r/s =t/u (which is a rational number)

# Commutative property

Changing the order of operands in addition of rational numbers does not change the result. Hence, rational numbers under addition are commutative.

Let's take p/q, r/s as an example;

p/q + r/s = r/s + p/q

where LHS=RHS

# Associative property

Even though if we add numbers regardless of how they are grouped. In both the groups the sum is the same.

Let's take p/q, r/s and t/u as an example;

p/q + (r/s + t/u) = (p/q + r/s)+ t/u

where LHS=RHS

Addition holds for all these properties and thus can be concluded that rational numbers are closed under addition