HELPPPP!!!! sepcific
explanation is best !!! this is discrete mathematics content.
HELPPPP!!!! sepcific explanation is best !!! this is discrete mathematics content. 1. Prove, or disprove by...
Discrete Math
□ Prove or disprove: If n is any odd integer then (-1)"--1 Problem 6:
Please prove this statement using indirect method of discrete mathematics. If n = ab, where a and b are positive integers, then a ≤ √n or b ≤ √n
discrete math question using proofs to determine to prove the
following equation or disprove it
4. Prove or disprove. Let A, B, C, and D be sets. Then (Ax B)n (CxD) (Ancx (B nD) 5. Prove or disprove: {2k 1 k E Q} {4" | k E Q) F6 7 Prove or disprove. Let A be a set and let I be an arbitrary index set for a collection of sets {Be l α E 1). Then, 6. An(UP)-a αΕΙ
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...
(1) Prove or disprove the following statements. (a) Let a, b and c be integers. If aſc and b|c, then (a + b)|c (b) Let a, b and c be integers. If aſb, then (ac)(bc)
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 +...
Discrete Mathematics Question 1: (a) Use the method of generalizing from the generic particular in a direct proof to show that the sum of any two odd integers is even. See the example on page 152 (4th edition, Discrete Mathematics with Applications) for how to lay this proof out. (b) Determine whether 0.151515... (repeating forever) is a rational number. Give reasoning. (c) Use proof by contradiction to show that for all integers n, 3n + 2 is not divisible by...
This is discrete mathematics.
I need answer and explanation for #28 #29 #30.
Thank you so much!!
28. Define an "onto" function. Give an example of an onto function from X = {1,2,3,4,5,6,7,8,9,0} onto Y = {a,b,c,d} 29. What is the domain and co-domain of the function which assigns to each pair of non- negative integers the first integer of the pair? What is the range? 30. Let S be the set of all positive integers not exceeding 100. Let...
1. Let a, b,cE Z be positive integers. Prove or disprove each of the following (a) If b | c, then gcd(a, b) gcd(a, c). (b) If b c, then ged(a., b) < gcd(a, c)
1 point Prove the following statement: If n2 is even, then n is even. Order each of the following sentences so that they form a logical proof. Proof by Contrapositive: Choose from these sentences: Your Proof: Suppose n is odd. Then by definitionn 2k +1 for some integer k Required to show if n is not even (odd), then n is not even (odd). Thus n2(2k1)2. n24k2 4k1. 22(22+2k) +1 Thus n2 (an integer) +1 and by definition is odd....