Consider the universal conditional: ∀r∈Qc,s∈Q,r+s∈Qc Note: Q is the set of all rational numbers; Qc is the set of all irrational numbers. Prove the statement is true using the proof method, "Proof by contradiction." You must use the proof method contradiction and within it you must show you understand the formal definition of rational and irrational numbers.
Consider the universal conditional:
∀r∈Qc,s∈Q,r+s∈Qc
Note: Q is the set of all rational numbers; Qc is the set of all irrational numbers.
Prove the statement is true using the proof method, "Proof by contradiction."
You must use the proof method contradiction and within it you must show you understand the formal definition of rational and irrational numbers.
Because of the limitations of Canvas, you should write your proof as a sequence of formal statements with English-language justifications. You do not need to create a Canvas table.
For full credit, justify every statement and explicitly begin and end the proof as shown in lectures.
If you find it is too hard to use the Canvas Insert Math Tool, then formalize in English. For example, in the problem statement, in place of the formal statement, I could have written:
If r is an irrational number and s is a rational number, then the sum of r and s is an irrational number.
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