# Discrete Math Question Prove the following statement: "The sum of any two rational

Discrete Math Question
Prove the following statement:
"The sum of any two rational numbers is rational."

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Arham Warner

Step 1
Concept Used:
A rational number is the number that can be written in the form $$\displaystyle{\frac{{{a}}}{{{b}}}}$$ where , a and b are integers and $$\displaystyle{b}\ne{}{0}$$
Step 2
Proof:
We want to prove that the sum of two rational numbers is rational
Let $$\displaystyle{x}={\frac{{{a}}}{{{b}}}}$$ where $$\displaystyle{b}\ne{0},{a},{b}$$ are integers
and $$\displaystyle{y}={\frac{{{a}}}{{{b}}}}$$ where $$\displaystyle{d}\ne{0},{c},{d}$$ are integers
consider
$$\displaystyle{x}+{y}={\frac{{{a}}}{{{b}}}}+{\frac{{{c}}}{{{d}}}}$$
Since a,b,c,d are integers then $$\displaystyle{a}{d}+{b}{c}$$ and bd is integer and $$\displaystyle{b}\ne{}{0},{d}\ne{}{0}\Rightarrow{b}{d}\ne{}{0}$$
$$\displaystyle\Rightarrow{x}+{y}$$ rational
hence proved.