5.3.6 Here is a 'proof' that all human beings have the same age. Where is the flaw in the argu- ment? 1) In a set with only 1 person, all the people in the set have the same age. Proof. (Base case n = (Inductive hypothesis) true that all of the people in the set have the same age. Suppose that for some integer n > 1 and for all sets with n people, it is (Inductive step) Let A be a set with n+1 people, say A = {a1,...,an, an+1}, and let A' = {a1,...,an} and A" = {a2, ...,an+1}. The inductive hypothesis tells us that all the people in A' have the same age and all the people in A" have the same age. Since a2 belongs to both sets, then all the people in A have the same age as a2. We conclude that all the people in A have the same age. (Conclusion) By induction, the claim holds for all n > 1.

5.3.6 Here is a 'proof' that all human beings have the same age. Where is the flaw in the argu- ment? 1) In a set with only 1 person, all the people in the set have the same age. Proof. (Base case n = (Inductive hypothesis) true that all of the people in the set have the same age. Suppose that for some integer n > 1 and for all sets with n people, it is (Inductive step) Let A be a set with n+1 people, say A = {a1,...,an, an+1}, and let A' = {a1,...,an} and A" = {a2, ...,an+1}. The inductive hypothesis tells us that all the people in A' have the same age and all the people in A" have the same age. Since a2 belongs to both sets, then all the people in A have the same age as a2. We conclude that all the people in A have the same age. (Conclusion) By induction, the claim holds for all n > 1.

Name: 5.3.6 Here is a 'proof' that all human beings have the same age. Wher
Uploaded: 2024-03-05T11:53:49.000Z
Channel: Bartleby
Description: 5.3.6 Here is a 'proof' that all human beings have the same age. Where is the flaw in the argu-ment?Proof. (Base case n = 1) In a set with only 1 person, all the people in the set have the same age.(Inductive hypothesis) Suppose that for some intege

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

صورة 1. Which of the following pairs of sets are disjoint and which are not ? (i) {x: x is an even natural number), {y:y is an odd natural number} (ii) {x : x is a prime number and divisor of 12}, {y:ye N and 3sy55} (iii) {x :x is a king of 52 playing cards}, { y: y is a diamond of 52 playing cards} (iv) {1, 2, 3, 4, 5}, (a, e, i, o, u} 2. Find the intersection of A and B in each of the following : (i) A = {x:xeZ), B= {x:xe N) (ii) A= {Ram, Rahim, Govind, Gautam} B = {Sita, Meera, Fatima, Manprit} 3. Given that A {1, 2, 3, 4, 5}, B={5, 6, 7, 8, 9, 10} find (i) A UB (ii) AB- 4. If A ={x: xe N }, B={y:ye z and -10s ys0} find A UB and write your answer in the Roster form as well as set-builder form. 5. If A ={2, 4, 6, 8, 10}, B (8, 10, 12, 14}, C ={14, 16, 18, 20}. Find (i) A U(BUC) i) An(BnC). Let U = {1, 2, 3,. 10), A (2, 4, 6, 8, 10}, B = ( 1,3, 5, 7, 9, 10} Find () (AUB)' (i) (AOB)' (i) (B') (iv) (B-A). 7. Draw Venn diagram for each the following: 7/11 6.
Given a positive integer n, let a1,n ... a2,n–1 a2,n ... a3,n–2 аз,п—1 a3,n .. An = аn-1,2 ап-1,n-2 аn-1,n-1 An-1,n ... an,1 An.2 An,n-2 An,n-1 An,n ... whose aij entries with i+j
7. Suppose we know that each of An, n ≥ 0, is countable. Show that (a {A0, A₁,..., An,...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! 8. (b) (c) Prove that U20 A, is countable. Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words. Prove that the relation between sets is symmetric and transitive.
"for all natural numbers m, n, p, we have that if p | (m * n) then either p | m or p | n" Try different concrete values for m, n, and p. Is this a true statement or a false statement? If false, give a counterexample. If true, find a proof.
7. Suppose we know that each of An, n ≥ 0, is countable. Show that (a)) {A0, A₁, A,...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! ES) Prove that U20 A; is countable. (c) Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words.
If A and B are two sets in M with Ac B.Then m AsB this is property monotenicity. If A and B are two sets in M with A c B, then mA smA +m (B\A)= mB If A and B are two sets in M with Ac B, then mAsmA +m (A B) = mB If A and B are two sets in M with A c B, then mAsmA + m (B\A)2 m B.
Please explain Thanks!
3) Let M be the set of all the words you can get by switching the letters in ENANNANANANAS How many words in M contain neither ANAS nor ENA? For example. SNANNANANANAE Bad words are for example ENANNANANANAS, SENANNANANANA, and NNNNENANASAAA.
The subject is mat 107 I am doing a worksheet for Notes for sets and Venn Diagrams. The question is The entire field of mathematics boils ddown to the assumption of a set of ----------? Then there is another question An axiom is a ------ (or statement) regarded as self-evidently true with out proof.
Nine students, five men and four women, interview for four summer internships at a city newspaper.(a) In how many ways can the newspaper choose a set of four interns?(b) In how many ways can the newspaper choose a set of interns with two men and two women?(c) How many set can be formed such that all interns are not of the same sex?
Which of the following sets is NOT well-defined?: -The set of correct answers in the exam. -The set of nice students in the class. -The set of all counting numbers less than π. -The set of prime numbers
Which of the following is the set P for all prime numbers less than 14? P={2,3,5,7,11,13} P={1,2,3,5,7,11,13} P={2,4,6,8,10,12} P={2,4,6,8,10,12,14}