Please send me the solutions for the above 6 questions. Please send it as tomorrow I have an exam. Thank You. ?
Please send me the solutions for the above 6 questions. Please send it as tomorrow I...
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...
Using discrete mathematical proofs: a. Prove that, for an odd integer m and an even integer n, 2m + 3n is even. b. Give a proof by contradiction that 1 + 3√ 2 is irrational.
1) Prove for any integer n, if n2 is a multiple of 6 then so is n. To get credit, you should use the following facts in your proof: If n2 is even then so is n. (Proved) If n2 is a multiple of 3, then so is n. (Proved) 2)By contradiction, prove that the square root of 6 is irrational. The result of part 1 should be be used as Lemma in your proof.
1. Formalize the following argument by using the given predicates and then rewriting the argument as a numbered sequence of statements. Identify each statement as either a premise, or a conclusion that follows according to a rule of inference from previous statements. In that case, state the rule of inference and refer by number to the previous statements that the rule of inference used.Lions hunt antelopes. Ramses is a lion. Ramses does not hunt Sylvester. Therefore, Sylvester is not an...
Only need 2-5. Need it done ASAP, thank you in advance!! Proofs 1) (1.7.16) Prove that if m and n are integers and nm is even, then m is even or n is even. * What is the best approach here, direct proof, proof by contraposition, or proof by contradiction why? * Complete the proof. 2) Prove that for any integer n, n is divisible by 3 iff n2 is divisible by 3. Does your proof work for divisibility by...
For Exercises 1-15, prove or disprove the given statement. 1. The product of any three consecutive integers is even. 2. The sum of any three consecutive integers is even. 3. The product of an integer and its square is even. 4. The sum of an integer and its cube is even. 5. Any positive integer can be written as the sum of the squares of two integers. 6. For a positive integer 7. For every prime number n, n +...
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0. ________(b) m, n in N, 5m 2n is in N. ________(c) x in R, if |x − 2| < 3, then |x| < 5. #8. For each statement, (i) write the statement in logical form with appropriate variables and quantifiers, (ii) write the negation in logical form, and (iii) write the negation in a clearly worded unambiguous English sentence....
Discrete Math: Prove that there can be no perfect square between 25 and 36, i.e. there is no integer n so that 25 < n2 < 36. Prove this by directly proving the negation. Your proof must only use integers, inequalities and elementary logic. You may use that inequalities are prsered by adding a number on both sides, or by multiplying both sides by a positive number. You cannot use the square root function. Do not write a proof by...
The Fibonacci Sequence F1, F2, ... of integers is defined recursively by F1=F2=1 and Fn=Fn-1+Fn-2 for each integer . Prove that (picture) Just the top one( not 7.23) n 3 Chapter 7 Reviewing Proof Techniques 196 an-2 for every integer and an ao, a1, a2,... is a sequence of rational numbers such that ao = n > 2, then for every positive integer n, an- 3F nif n is even 2Fn+1 an = 2 Fn+ 1 if n is odd....
1.)Which of the expressions is equivalent to the following statement: The sum of two even numbers is even. a.) If x is even or y is even, then x + y b.) If x is even or y is even, then x + y is even c.) If x is even and y is even, then x + y is not even. d.) If x is even and y is even, then x + y is even 2.) Find a...