Question: Al says he can prove that all sheep in a flock are the same color: Base case: One sheep. It is clearly the same color

Al says he can prove that all sheep in a flock are the same color:

Base case: One sheep. It is clearly the same color as itself.
Induction step: A flock of n sheep. Take a sheep, a, out. The remaining n−1 are all the same color by induction. Now put sheep a back in and take out a different sheep, b. By induction, the n−1 sheep (now with a) are all the same color. Therefore, all the sheep in the flock are the same color. What is wrong with Al’s “justification”?

Step by Step Solution

★★★★★

3.44 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The induction assumes that the set of n1 shee... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Introduction to Algorithms Questions!

Cheadle Company purchased a fleet of 20 delivery trucks for $8,000 each on January 2, 2019. It decided to use composite depreciation on a straight-line basis and calculated the depreciation from the...

There are four basic operations on red-black trees that perform structural modifications: node insertions, node deletions, rotations, and color modifications. We have seen that RB-INSERT and...

Draw an ERD for each of the following situations. (If you believe that you need to make additional assumptions, clearly state them for each situation.) Draw the same situation using the tool you have...

A compare-exchange operation on two array elements A[i] and A[j], where i A[j] 2 exchange A[i] with A[j] After the compare-exchange operation,...

please show all work for your answers, Thanks. C-4.48 Al says he can prove that all sheep in a flock are the same color: Base case: One sheep. It is clearly the same color as itself. Induction step:...

Induction Proof: Consider the following induction "proof" that all sheep in a flock are the same color: Base Case: One sheep. It is clearly the same color as itself. Induction step: A flock of n...

C-1.15 Consider the following induction "proof" that all sheep in a flock are the same color: Base case: One sheep. It is clearly the same color as itself. Induction step: A flock of n sheep. Take a...

If you know how to prove things by induction, then here is an amazing fact: Theorem. All horses are the same color. Proof. We'll induct on the number of horses. Base case: 1 horse. Clearly with just...

Analyze the case Espinoza v. Arkansas Valley Adventures. This is a very clear, well-written, and well-reasoned case written by Neil Gorsuch, who was since appointed to the U.S. Supreme Court. - what...

CLOSING ARGUMENTS A Closing Argument should: 1. Repeat your theory and theme of the case 2. Summarize the evidence that preceded it 3. Relate the evidence to the law and the legal issues (i.e....

When we use the integration by parts to integrate Ban-ly dx we obtain an expresston of the form A - ( B. dr. Find B. 1 x(1+x?) 1 x1-x? x?(1+x?)

PREPARE 1. TRIAL BALANCE 2. LEDGER DATE 2020, Aug 1 PARTICULARS Cash De Leon, Capital Office Supplies Cash 2 Taxes and Licenses Cash 3 Cash 4 Furniture and Fixtures Computer Cash DR Loan, Capital -...

lim h 0 1 ( x h ) 2 - 1 x 2 h

A flexible chain weighing 40.0 N hangs between two hooks located at the same height (Fig. P12.19). At each hook, the tangent to the chain makes an angle θ= 42.0° with the horizontal. Find...

A 4-lb ball B is traveling around in a circle of radius r1 = 3 ft with a speed (vB)1 = 6 ft/s. If the attached cord is pulled down through the hole with a constant speed vr = 2ft/s, determine how...

A particle with a mass of 2.00 x 10-16 kg and a charge of 30.0 nC starts from rest, is accelerated by a strong electric field, and is fired from a small source inside a region of uniform constant...

An 820-turn wire coil of resistance 24.0 Ω is placed around a 12 500-turn solenoid 7.00 cm long, as shown in Figure P32.68. Both coil and solenoid have cross-sectional areas of 1.00 x 10-4 m2....

This problem extends the reasoning of Section 26.4, Problem 26.37, Example 30.6, and Section 32.3. (a) Consider a capacitor with vacuum between its large, closely spaced, and oppositely charged...

1. The psychodynamic and learning perspectives agree that dissociative identity disorder symptoms are ways of dealing with anxiety. How do their explanations differ?

Professor Diogenes has n supposedly identical integrated-circuit chips that in principle are capable of testing each other. The professor?s test jig accommodates two chips at a time. When the jig is...

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T (n) = T (n 1) + T (n/2) + n. Use the substitution method to verify your answer.

How quickly can you multiply a kn n matrix by an n kn matrix, using Strassens algorithm as a subroutine? Answer the same question with the order of the input matrices reversed.

Need help solving; A put option that expires in six months with an exercise price of $75 sells for $4.55. The stock is currently priced at $71, and the risk-free rate is 4.1 percent per year,...

26. To qualify for a police academy, candidates must score in the top 20% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to...

One can use a fitted logistic regression model to predict the probability/odd of an interest of choice represented by an dependent variable given a set of the values of the independent variables in...