Prove that n-Cube Qn is not planar for n>=4.

I need to prove the n-cube Qn is not planar for n greater than or equal to 4.

Planar graph

I need to show that if G is a planar graph, then G must have a vertex of degree at most 5.

Discrete Math: Logic

Please see the attached file for the fully formatted problems. Discrete Math True or False questions 1. Circle T if the corresponding statement is True or F if it is False. T F The Fibonacci Sequence is {sn | sn = sn1 + sn2, with s0 = 1 and s1 = 1}. T F The First (Weak) and Second (Strong) Principles of Mathematical Induction are logically equivalent. T F All recursively defined sequences of Integers take on successively larger values. T F If lazy students fail CMSC203 and Paul passed CMSC203, then we can conclude logically that Paul is not lazy. T F Functions that are O(x2) grow faster than functions that are O(2x). T F The product of a Rational and an Irration... click for more

Equivalence Relations

Verify that each of the following are equivalence relations on the plane R^2 (where R are real numbers) and describe the equivalence classes geometrically. 1) (x1,y1)R(x2,y2) if and only if x1 = x2 2) (x1,y1)R(x2,y2) if and only if x1 + y1 = x2+y2 3) (x1,y1)R(x2,y2) if and only if x1^2 + y1^2 = x2^2 + y2^2

Combinations, Permutations and Truth Tables

1. (a) How many license plates can a state produce if the plates can contain 6 characters (from 26 letters and 10 digits) if they can only use one digit? (b) How many ways can Mr. Paul choose 6 students from a class of 15 Boys and 12 Girls, if he must choose at least 5 boys? (c) How many orderings are there of the letters of the word STRAWBERRYALARMCLOCK ? (d) How many ways can I seat 12 people around a circular table, if a certain pair of people cannot sit next to one another? (e) How many ways can I fill a box of 50 chocolates from 10 types if I must have at least 1 of each type in the box? 3. (a) For a collection of 80 coins, if 53 are quarters, 15 are quarters from the 1... click for more