tell me the answer,don't explain
tell me the answer,don't explain Outline a proof of the following statement by writing the "starting...
please help me make this into a contradiction or a direct proof please. i put the question, my answer, and the textbook i used. thank you also please write neatly proof 2.5 Prove har a Simple sraph and 13 cdges cannot be bipartite CHint ercattne gr apn in to ertex Sets and Court tne忤of edges Claim Splitting the graph into two vertex, Sets ves you a 8 Ver ices So if we Change tne书 apn and an A bipartite graph...
In the following problem, we will work through a proof of an important theorem of arithmetic. Your job will be to read the proof carefully and answer some questions about the argument. Theorem (The Division Algorithm). For any integer n ≥ 0, and for any positive integer m, there exist integers d and r such that n = dm + r and 0 ≤ r < m. Proof: (By strong induction on the variable n.) Let m be an arbitrary...
Proofs Use the following definitions and facts about integers in writing your proofs. . Suppose n є Z. We say n is odd if there exists k є Z such that n-2k + 1 . Suppose n є Z. We say n is even if there exists ke Z such that n-2k . Suppose m, n є Z and m -0. We say ma divides n (written mln) if there exists k Z such that n mk. is either ever...
please answer questions #7-13 7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
You're the grader. To each "Proof", assign one of the following grades: A (correct), if the claim and proof are correct, even if the proof is not the simplest, or the proof you would have given. C (partially correct), if the claim is correct and the proof is largely a correct claim, but contains one or two incorrect statements or justifications. . F (failure), if the claim is incorrect, the main idea of the proof is incorrect, or most of...
I need help with this problem DO 11 CLOD04 W 5000 DOLIUL CLIOUTOU DO 10 DOIS DILIDUL Exercise 19. Adapt the proof of Theorem 30 to show that if n = 2 mod 4 then there is no r e such that p2 = n. This shows, for example, that 10 is irrational. Remarl. 6 Ono con monoralizo the above thoorom to show that if n 7 is Theorem 30. There is no r EQ with the property that p2...
From the proof of (ii) . Explain/Show why -n+ 1Sm-kn-1 is true by construction. . Explain/Show why 0 is the only number divisible by n in the range -n+1 ton-1 Proposition 6.24. Fix a modulus nEN. (i) is an equivalence relation on Z. (ii) The equivalence relation-has exactly n distinct equivalence classes, namely (ii) We need to prove that every integer falls into one of the equivalence classes [0], [1],..., [n -1], and that they are all distinct. For each...
3. Let W = P({1,2,3,4,5}). Consider the following statement and attempted proof: VAE W WB EW (((AUB) C A) + (ACB)) (1) Towards a universal generalization argument, choose arbitrary A € W, BEW. (2) We need to show ((AUB) C A) + (ACB). (3) Towards a proof by contraposition, assume B CA, and we need to show A C (AUB). (4) By definition of subset inclusion, this means we need to show Vc (E A →r (AUB)). (5) Towards a...
Discrete Math - Please be detailed. Thanks! . Below is one of the classic fallacies. Note that each step is justified. This is the amount of details we would like to see in your proofs. Identify the fallacious step and explain. 5 points STEP 1: Let ab. STEP 2: Multiply both sides by a, we get a2 ab STEP 3: Add a2 to both sides, we get a2 + a2-ab + a2b STEP 4: Collecting like terms, we get 2a2...
1) Webber Chap. 11 Exercise 1 Prove that {a"b"c"} is not regular. Hint: Copy the proof of Theorem 11.1-only minor alterations are needed. Theorem 11.1 The language {a"b"} is not regular. • Let M = (Q, {a,b}, 8, 9., F) be any DFA over the alphabet {a,b}; we'll show that L(M) + {a"b"} • Given as for input, M visits a sequence of states: - *(q,,ɛ), then 8*(q,,a), then 8*(9,,aa), and so on • Since Q is finite, M eventually...