Show that any group of 20 people will at least have one pair of members who have the same number of friends. (Here, you can let be an arbitrary set of 20 people, and define for to be the number of friends for person within this group. Assume friendship is symmetric, so if someone has 0 friends in the group then there cant
In how many ways can a 10-question true-false exam be answered? (Assume that no questions are left blank)
Discrete Mathematics Basics
1) Find out if the relation R is transitive, symmetric, antisymmetric, or reflexive on the set of all web pages.where if and only if
I)Web page a has been accessed by everyone who has also accessed Web page b.
II) Both Web page a and Web page b lack any shared links.
III) Web pages a and b both have at least one shared link.
An Example with Intervals
Let the universal set be the set R of all real numbers and let
a) Find
b) Find
c) Find
Let G be the graph with vertices
To find the number of walks of from
Although tea is the world’s most widely consumed beverage after water, little is known about its nutritional value. Folacin is the only B vitamin present in any significant amount in tea, and recent advances in assay methods have made accurate determination of folacin content feasible. Consider the accompanying data on folacin content for randomly selected specimens of the four leading brands of green tea.
(Data is based on “Folacin Content of Tea,” J. Amer. Dietetic Assoc., 1983: 627–632.) Does this data suggest that true average folacin content is the same for all brands? a. Carry out a test using α=.05α=.05 via the P-value method. b. Assess the plausibility of any assumptions required for your analysis in part (a). c. Perform a multiple comparisons analysis to identify significant differences among brands.