Question: Consider the statement: If two positive integers a and b are picked such that a b and b | a then a = b. 1.

 Consider the statement: If two positive integers a and b are

Consider the statement: If two positive integers a and b are picked such that a b and b | a then a = b. 1. Formalize the statement. Use the insert "math equation tool (1 )." (See below about formalizing in English if you have difficulty with the tool.) 2. Prove the statement is true using the combined proof methods, "Proof by contradiction" and "Proof using definitions." You must use contradiction and you must use the formal definition from class for divisibility. 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 class. For example, if I wanted to prove this statement using a direct proof, I would start with the statement, Va, beZ+, (a | b) A (6 | a) a= b To be proved. and end with the statement, :: Va, b e Z+, (a | b) A (6 | a) a=b By proof by contradiction. If you find it is too hard to use the Canvas "insert math tool" then formalize in English. In my example I would have written, For all a,b positive integers, a | b and ba -> a = b To be proved. Therefore, for all a,b positive integers, ab and bl a -> a = b By proof by contradiction

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