We wish to prove the following statement: For all integers a and b, if 5 divides...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
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
Expert Answer:
Answer rating: 100% (QA)
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
Posted Date:
Students also viewed these mathematics questions
-
For the vectors A and B if Fig. 1.34, use a scale drawing to find the magnitude and direction of (a) The vector sum A + B and (b) The vector difference A B. Use your answers to find the magnitude and...
-
Find the angle between A and B if A = 1.00i + 2.00j + 1.00k and B = 1.00i 1.00k.
-
Find the angle between A and B if A = 3.00i + 2.00j + 1.00k and B = 1.00i + 2.00j + 3.00k.
-
Problem 5: Closing entries. (10 points) Given the following accounts, prepare the closing entries in the order and method taught using Income Summary. Number each entry 1, 2, .... Accounts payable $...
-
Refer to the information in Exercise 6.25. REQUIRED A. Calculate the number of units started during the month. B. Calculate the equivalent units for direct materials and conversion costs under the...
-
In benzaldehyde, two of the ring protons have resonance at 7.87 ppm, and the other three have resonance in the range from 7.5 to 7.6 ppm. Explain.
-
Stock markets are merely casinos allowing speculators to get rich while doing nothing for ordinary people like you and me. Write an essay explaining why you agree or disagree with this statement.
-
Becky Company borrows $60,000 on July 1 from the bank by signing a $60,000, 10%, one-year note payable. (a) Prepare the journal entry to record the proceeds of the note. (b) Prepare the journal entry...
-
Q3 Specify null and alternative hypotheses (total three sets) Run two-way ANOVA to test hypotheses. State your statistical conclusion If you find the interaction effect significant (i.e., reject the...
-
In a paint mixing plant, two tanks supply fluids to a mixing cistern. The height, h, of the fluid in the cistern is dependent upon the difference between the input mass flow rate, q, and the output...
-
Determine the percent of a standard normal distribution N( = 0; o = 1) is found in each region. Be sure to draw a graph. Write your answer as a percent rounded to the nearest tenth. a) The region Z <...
-
Use conservation of energy to solve the following problems. Your final conservation of energy equation must be shown. 3.) A ball starts at the top of a slide at point A with an initial velocity of...
-
The company's consolidated statement of income is provided below: (in millions of dollars) Revenues Sales by company-operated restaurant stores Revenue from franchised stores Total revenues Years...
-
Explain, consisting of a minimum of 200 words, on the significance of Operations Specifications for air carriers. Share your perspective on the potential consequences if airlines were not required to...
-
HFA has two program departments, one for the treatment of ex - convicts who are drug users and the other for a job training program for ex - convicts. The treatment pro - gram hires 4 0 % of the...
-
9. You go to the gym 5 times a week, and each time you are there you bench press 80.0kg thirty times. Each time you are lifting the barbell basically the length of your arm (about 0.80m). a. Over the...
-
0.0/1.4 points (graded) Which groups of genetic markers often appear together in people?
-
What can scientists learn by comparing the fossilized skeletons of extinct primates with the bones of modern species?
-
Aussie Steaks Inc. operates a chain of steak restaurants in the United States. On January 1, 2015, the company had \($500\) million in assets. On January 1, 2015, the company acquired 25 percent of...
-
On January 1, 2015, Tradiciones, Inc., established Tradiciones de Mexico, a wholly-owned, self-sustaining Mexican subsidiary with assets valued at 48 million pesos. The peso (P) is the functional...
-
Global Enterprises Corporation (GE) is a manufacturing company whose principal products are microwave ovens, refrigerators, and conventional ovens. The company had a long history of selling...
Study smarter with the SolutionInn App