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Discrete Math

Fractions in Binary

There are fractions in binary (floating points). Please convert 1.1 subscript 2 to decimal. Kindly show the steps. Thanks.

Euclidean Algorithm

Please see attached file for full problem description. 1. Use the euclidean algorithm to find gcd(729,75), then rerun the algorithm to find integers m and n such that gcd(729,75) = 729m + 75n. 2. Find the prime factorizations of (482,1687). Thus find the gcd and the lcm of the pair. Also find the gcd by Euclid's algorith

Trace proof

Suppose T in L(V). Prove that if trace(ST) = 0 for all S in L(V), then T = 0.

Statistics and Sampling

A survey of 100 students has the following results : 70 of the students stated they are pursuing at least one of the degrees: Mathematics, Computer Science, or Electrical Engineering. 40 were pursuing a Mathematics degree, 50 were pursuing a Computer Science degree, and 25 were pursuing an Electrical Engineering degree. 23 stu

Sets and Binary Relations : Equivalence Relations

2. Let A be the set { 1,2,3,4,5,6} and R be a binary relation on A defined as : {(1,1), (1,3), (1,5), (2,2), (2,6), (3,1), (3,3), (3,5), (4,4), (5,1), (5,3), (5,5), (6,2), (6,6)} (a) Show that R is reflexive. (b) Show that R is symmetric. (c)Show that R is transitive. 3. Let A be the set {1,2,3,4,5,6} and let F be t

Exact Sequences

If N and P are submodules of M that is an R-module and modules (N intersects P) and (N+P) are finitely generated then show that modules N and P are finitely generated.

Relations: reflexive, antisymmetric, transitive

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?

In a street there are 5 houses, painted 5 different colors.

1. In a street there are 5 houses, painted 5 different colors. 2. In each house lives a person of different nationality. 3. These five homeowners each drink a different kind of beverage, smoke different brand of cigar and keep a different pet. THE QUESTION: WHO OWNS THE FISH? HINTS: 1. The Brit lives in a red house

Set Partitions : Coarseness and Fineness

The meet of the partitions f1,...,fI is the finest partition that is coarser then each fi. The join of the partitions f1,...,fI is the coarsest partition that is finer than each fi. The meet of partitions is denoted and the join of partitions is denoted I

Binary Bits

Part A: Use 2's complement to represent - 1910 (using 6 binary bits)? Part B: Use 2's complement representation to calculate 510 - 1910 (using 6 binary bits)? See attached file for full problem description.

Venn Diagrams, Probability and Combinations

1. In an experiment, a pair of dice is rolled and the total number of points observed. (a) List the elements of the sample space (b) If A = { 2, 3, 4, 7, 8, 9, 10} and B = {4, 5, 6, 7, 8} list the outcomes which comprise each of the following events and also express the events in words: A, A  B, and A &#616

Logic : Truth and Lies

Knight = always says the truth knave = always lying Assume there are only knight and knaves. Suppose A says: " B and C are of the same type". Then you ask C " Are A and B of the same type?" What does C answer?

Logic Problems

1. Determine whether ~ [~ (p V ~q) <=> p V ~q. Explain the method(s) you used to determine your answer. 2. Translate the following argument into symbolic form. Determine whether the argument is valid or invalid. You may compare the form of the argument to one of the standard forms or use a truth table. If Spielberg is t

Find the bad coin out of given 8 coins using only a pan balance.

Eight coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. Describe an algorithm that identifies the bad coin in at most three weighings and also determines whether it is heavier or lighter than the others, using only a pan balance.

Truth Table

Construct a truth table for ~ p ^ (p ═ ═ > q), which is read; not p AND (p implies q)

Game Theory : Matrix, Population Formulation (Lions and Lambs)

In a population, there are two kinds of individuals, LIONS and LAMBS. Whenever two individuals meet, 40 yen is at stake. When two LIONS meet, they fight each other until one of them is seriously injured. While the winner gets all the money, the loser has to pay 120 yen to get well again. If a LION meets a LAMB then the LION take

Linear Operations

Need to figure out how to do this type of problem. Using A =[ Cos alpha - Sin alpha ] Sin alpha Cos alpha (1) Find A^-1 =[ ] E SO sub 2 (1R) (2) Check A inverse is in SO sub2 (R) Check A inverse * A = Identity and A *

5 Basic Finite Math Problems

Also as you can see in the attachments please change: page: 177 #1 x/nx page 230 #56. x + .04t(2nd power) + 3t + 5 page 269 #34 R(x) = 300/n (4x+1) page 303 #20 $125

Ordered Pairs and Operations on Sets

1. Recall that ordered pairs must have the property that (x,y) = (u,v) if and only if x = u and y = v. a) Prove that {{x}, {x,y}} = {{u}, {u,v}} if and only if x = u and y = v. Therefore, although we know that (x,y) does not equal {x,y} , we can define the ordered pair (x,y) as the set {{x}, {x,y}}. b) Show by an exa

Sets and Set Operations

4. Let A = {a, {a}, {{a}}} B = {ø, {a}, {a, {a}}} C = {a} Be subsets of S = {ø, a, {a}, {{a}}, {a, {a}}}. Find a) A C b) B C' c) A B d) ø B e) (B C) A f) A' B g) {ø} B 5. Let A = {x | x is the name of a former president of the US} B =