Sequences of Sets and Subsets

A sequence of sets S1, S2,…, Sn is given. Find a subset I of {1,2,…,n] such that the union of the corresponding sets Si has fewer elements than I does. 1. {1,2}, {2,3}, {5}. {1,3}, {4,5}, {4,5} 2. Five girls go into a library to get a book. Jennifer wants to read only The Velvet Room or Daydreamer. Lisa wants only Summer of ...continues

Matching

See Attachment. Tell whether the graph is bipartite....

Functions

Please see attachment. How can this be proved by mathematical induction?

Finding Maximum Number of Expected Sales

A supervisor has 5 salespeople who can be assigned to 5 different routes next month. Adam can be expected to sell $9000 worth of goods on Route 1, $8000 on Route 2, $10,000 on Route 3, $7000 on Route 4, and $8000 on Route 5. Betty would sell $6000. $9000, $5000, $7000, and $4000 on these routes; Charles would sell $4000, $50 ...continues

Triangle and Binomial Theorem

Following Pascal’s triangle and Binomial Theorem, evaluate the number c(12,7) - how? An example evaluation of c(8,5) = 56

Coefficient expansion

Evaluate the coefficient of x4 y9 in the expansion of (3x + y)13 How? An example evaluation of x6 y4 in the expansion of (x + 2y)10 = 32

Find the smallest positive integer with with exactly n different factors.

Find the smallest positive integer with exactly n different factors, for the following values of n. a) 3 b) 4

Connected Graph

Please see attached. I need help creating this picture in word, editable as a presentation object, or some similar editable format.

Proof of multiples

let m be a positive integer greater than or equal to 2. Prove that both the sum and product of two multiples of m are also multiples of m.

Counting

There are six sections of Math with a total enrollment of one hundred and ninety nine students, what is the smallest possible number of students in the section with the largest enrollment?