1. Prove with a direct proof or disprove by counterexample. If x is an odd 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...
Discrete Math
□ Prove or disprove: If n is any odd integer then (-1)"--1 Problem 6:
HELPPPP!!!! sepcific
explanation is best !!! this is discrete mathematics content.
1. Prove, or disprove by finding a counterexample: If a|bc where a,b and c are positive integers then a b or a c. 2. Let n be an odd integer. Show that there is an integer k such that n2 = 8k +1.
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.
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. (20pts) Prove or disprove each of the following statements. If true, then write a proof for the statement. If false, then give a specific explicit example. a) {12a + 4b: a and b are integers} = {4c: c is an integer), and b) For sets A, B and C: A(BUC)=(A\B)U(A\C).
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.
Prove or Disprove the following
Let x,y. If x + xy
+ 1 is even then x is odd
Give a proof or counterexample, whichever is appropriate. 1. For any sets A and B, (A ∩ B = ∅) AND (A ∪ B = B) ⇒ A = ∅ 2. An integer n is even if n2 + 1 is odd. 3. The converse of the assertion in exercise 62 is false. 4. For all integers n, the integer n2 + 5n + 7 must be positive. 1.65. For all integers n, the integer n4 + 2n2 − 2n...
Either prove or disprove (by giving a counterexample) this claim re- garding powersets and set containment: For any sets A and B, if A ⊆ B, then P(A) ⊆ P(B)