We wish to prove the following statement: For all integers a and b, if 5 divides...

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We wish to prove the following statement: For all integers a and b, if 5 divides a or 5 divides b, then 5 divides (5a + b). In this case, it is to attempt to find an example. In this case, it is to attempt an exhaustive check. The following is an example of The premise P(n) is true for all integers a and b where either 5 divides a or 5 divides b. Let a = 10 and b = 4. In this case the premise is true. Substituting for a and bwe get 5a + b = 54 which is Therefore, the original statement has been appropriate not appropriate not feasible feasible proof using counterexample divisible by 5 not divisible by 5 proven disproven proof by contradiction proof using contra-positive statement We wish to prove the following statement: For all integers a and b, if 5 divides a or 5 divides b, then 5 divides (5a + b). In this case, it is to attempt to find an example. In this case, it is to attempt an exhaustive check. The following is an example of The premise P(n) is true for all integers a and b where either 5 divides a or 5 divides b. Let a = 10 and b = 4. In this case the premise is true. Substituting for a and bwe get 5a + b = 54 which is Therefore, the original statement has been appropriate not appropriate not feasible feasible proof using counterexample divisible by 5 not divisible by 5 proven disproven proof by contradiction proof using contra-positive statement

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To prove or disprove the statement For all integers a and b if 5 divides a or 5 divides b then 5 div... View the full answer