Question

Please prove by: direct, cases, contra positive, contradiction,

or induction. Indicate which proof method used.
(a) If ( a=15 ) and ( b=5 ) then write down the elements in the set ( A={a-x b mid x in mathbb{Z}, a-x b eq 0} ).
(b) If ( a=17 ) and ( b=5 ) then write down the elements in the set

Answer 1

The question contains insufficient information to provide an exact set of elements or specific proof method. A more detailed context is needed to give a full answer.

Step-by-step explanation:

The question seems to be asking for help in determining the elements of a particular mathematical set given certain conditions for the values a and b. However, there's inadequate context to form a precise set or carry out a concrete proof. Nevertheless, I can explain how to approach a proof when more information is provided.

For a proof by cases, you split the argument into a limited number of cases and prove that the statement is true for each case. A proof by contrapositive argues that if the consequence of a statement is false, then the assumption must also be false. A proof by contradiction assumes the opposite of what you want to prove and shows that this leads to a logical inconsistency. Lastly, an induction proof establishes the base case and then shows that if the statement is true for one case, it is true for the next case as well.

The provided context includes assorted mathematical statements and assumptions that do not directly clarify what the student needs. Therefore, I recommend that the student provide additional details for a valid and accurate response.