Probability Game of Shooting

In a single duel, Shooter A hits target with a probability of 1/3. B with 1/2. C never misses. ABC fire in turns, A going first, B next, and C last. Shooting cycle repeats until only one dueler has not been hit. Use random # x, where 0 <= x <=1. What happens if the shooter hits the deadliest shooter first? in 10,000 du ...continues

Bit Strings

(a) How many bit strings of length 6 are there? Explain fully. (b) How many bit strings of length 6 are there which begin with a 0 and end with a 0? Explain fully. (c) How many bit strings of length 6 start with a 0 bit or end with a 0 bit? Explain fully.

Combinations

A women has 9 close friends. (a) In how many ways can she invite five of these to dinner? Explain/Show work. (b) Repeat part (a) with the added stipulation that two of her friends do not like each other so that if she invites one of them she cannot invite the other. Explain/Show work. (c) Repeat part (a), assuming ...continues

Binomial theorem and expanding a polynomial

Use the Binomial Theorem to write the expansion of (x + y)^6

Haase Diagram

Haase Diagram: (a) List the ordered pairs that belong to the relation. (b) Find the (boolean) matrix of the relation. See attached file for full problem description.

Matrices

Matrices: (a) Interpret the above matrices with respect to the above relations. (b) Compute , and use this matrix to determine which courses will have tutors available on which days. (c) Multiply the above matrices using regular arithmetic. Can you interpret this result? See attached file for full problem description.

Ordered Pairs

Describe R by listing the ordered pairs in R and draw the digraph of this relation. See attached file for full problem description.

A binary relation R is defined in terms of a given matrix. Define what it means for a relation to be (a) reflexive, (b), antisymmetric, and (c) transitive. Also, determine which of these are properties of R.

For the set A = {a, b, c}, let R be the relation on A which is defined by the following 3 by 3 matrix M_R: ---------------------------------------- Row 1: 1 0 1 Row 2: 1 1 0 Row 3: 0 1 1 ----------------------------------------- Which of the properties (reflexive, antisymmetric, transitive) are satisfied by R? ...continues

A binary relation R is defined in terms of a given matrix. Determine the transitive closure of R.

For the set A = {a, b, c}, let R be the relation on A which is defined by the following 3 by 3 matrix M_R: ---------------------------------------- Row 1: 1 0 1 Row 2: 1 1 0 Row 3: 0 1 1 ----------------------------------------- Determine the transitive closure of R.

Let R be the relation defined on Matrix A. We have to draw the digraph of the transitive closure of R and use the digraph to explain connectivity. For complete description of the problem, please see the attached problem file.

Draw the digraph of the transitive closure of R and use the digraph to explain the idea of connectivity. Is this graph connected? What does connectivity mean? See attached file for full problem description.