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.
Using discrete mathematical proofs: a. Prove that, for an odd integer m and an even integer...
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...
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...
Discrete mathematics Prove that the product of an odd integer and an even integer is always even.
Please send me the solutions for the above 6 questions. Please send it as tomorrow I have an exam. Thank You. ? 8. Prove that if n is a perfect square, then n + 2 is not a perfect square. 9. Use a proof by contradiction to prove that the sum of an irrational number and a rational number is irrational 17. Show that if n is an integer and n3 + 5 is odd, then n is even using...
Prove that if m is an odd integer then there is an integer n such that n= 4m+ 1 or n= 4m+ 3. Use a proof by cases.
DISCRETE MATHEMATIC For question 1, Use mathematical induction to prove the statements are correct for n ∈ Z+(set of positive integers). 1. Prove that for n ≥ 1 1 + 8 + 15 + ... + (7n - 6) = [n(7n - 5)]/2 For question 2, Use a direct proof, proof by contraposition or proof by contradiction. 2. Let m, n ≥ 0 be integers. Prove that if m + n ≥ 59 then (m ≥ 30 or n ≥...
2: Use mathematical induction to prove that for any odd integer n >= 1, 4 divides 3n + 1 ====== Please type / write clearly. Thank you, and I will thumbs up!
3. Prove, by indirect proof, that if n is an integer and 3n+ 3 is odd, then n is even. Show all your work. (4 marks) MacBook Pro ps lock Command option control option command 20t3 la
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.
Consider the following statement: 2 ^ (1/3) , the cube root of 2, is irrational. (a) First, prove that if n^3 is even, then n is even, where n is an integer. (b) Now, using a proof by contradiction, prove that 2^(1/3) , the cube root of 2, is irrational.