Discrete Structures

1. How many bit strings of length ten contain either at least five consecutive 0's or at least five consecutive 1's? explain 2. Which is more likely: rolling a total of 8 when two dice are rolled, or rolling a total of 8 when three dice are rolled? explain 3. Three fair dice are rolled.Let X be the sum of the numbers that ...continues

Discrete Structures

Please see the attached file for full problem description.

Inverse of a Matrix

Find the inverse of a matrix. Matrix row 1 = [-1 2] row 2 = [1 3] Find the inverse of this matrix. a) Find A-1 b) Find A3 c) Find (A-1)3 d) Use your answers to (b) and (c) to show that (A-1)3 is the inverse of A3.

Compute each of these double sums?

(a) 3 3 Σ Σ (i - j) I = 1 j = 1 (b) 3 2 Σ Σ (3i + 2j) I = 0 j = 0

Function f: R --> R defined by f(x) = x3 - 5

Consider the following function f: R --> R defined by f(x) = x3 - 5 . (a) Use the contrapositive to explain (no proof necessary) that f is a one-to-one function. (b) Find f -1. (c) Compute f o f.

Matrix Computation

Here is the problem I need help with. Let A= -1 2 1 3 (a) Find A ^ -1 (b) find A ^ 3 (c) Find (A ^ -1) ^ 3 (d) (The part that really has me stumped) Use your answers to (b) and (c) to show that (a ^ -1) ^ 3 is the inverse of A ^ 3.

True or Fales

The cardinality of a power set is at least 1 ( )

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Please do (part.C)