Math Crossword Puzzles: Checker Tile Problems
The attached is 4 tables where you have to figure out the missing number. For each table, you can only use 0-9 numbers once (not including the given numbers).
The attached is 4 tables where you have to figure out the missing number. For each table, you can only use 0-9 numbers once (not including the given numbers).
Assume that n is a positive integer. Use the proof by contradiction method to prove: (a) If 7n + 4 is an even integer, then n is an even integer. (b) Prove: n is an even integer iff 7n + 4 is an even integer. (Note this is an if and only if (iff) statement.
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 ɨ
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?
Please see attached file. 1. (4pts) Let p, q, and r be the following statements: p: Roses are red q: The sky is blue r: The grass is green (a) p ^ q (b) p ^ (q  r) (c) q --> (p ^ r) (d) (~ r ^ ~ q) --> ~ p 2. (4pts) Write in symbolic form using p, q, r, , , , &#
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
1. Write the negation for the statement below. No one in the family eats rhubarb 2. Let p, q, and r be the following statements: p: Mike is sailing q: Alice is on vacation r: Sam is in town Translate the following statement into English: (p   q)  r 3. Write the following co
Logic 1. Let p, q, and r be the following statements: p: Roses are red q: The sky is blue r: The grass is green Translate the following statements into English (a) p  q (b) p  (q  r) (c) q  (p  r) (d) (  r   q)  
1. In a survey of 75 consumers, 12 indicated that they were going to buy a new car, 18 said they were going to buy a new refrigerator, and 24 said they were going to buy a new washer. Of these, 6 were going to buy both a car and a refrigerator, 4 were going to buy a car and a washer, and 10 were going to buy a washer and a refri
Explain what is meant by the sphere St () with centre i and radius / t in the vector space F. Show that... Let C be a linear [ri, k, dj-code over Fq and set t [i]. Show that... for all distinct elements 7 and of C. Hence show that... Give the definition of a perfect code. Give the definition of a coset leader/'Let C and t be
Please see the attached file for the fully formatted problems. (a) Explain what is meant by (i) a linear code over Fq (ii) the weight w(x) of a vector x (iii) the weight w(C) of a code. Prove that,... (b) Prove that w(C) = d(C) if C is a linear code. (c) Define F-linear equivalence of codes. State the three row and two
Consider the following activity-on-arc project network, where the 12 arcs (arrows) represent the 12 activities (tasks) that must be performed to complete the project and the network displays the order in which the activities need to be performed. The number next to each arc (arrow) is the time required for the corresponding acti
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.
Construct a truth table for ~ p ^ (p ═ ═ > q), which is read; not p AND (p implies q)
Using the Huffman code given in the attached image, (a) encode the string "NEEDLE". (b) decode the bit string "01111001001110".
Find a minimal spanning tree for the connected weighted graph, following Prim's algorithm. Please see attached 4.doc for the details on graph and Prim's algorithm for finding a minimal spanning tree.
[1] Encode "LEADEN" using the Huffman code tree given in the attachment. [2] What can you say about a vertex in a rooted tree that has no descendants? Please see the attachment for more tree related problems.
Let f: R-> R be a function that satisfies f(x+y) = f(x) + f(y) for all x,y in R. Suppose that f is continuous at some point c. Prove that f is continuous on R. How would you go about starting this proof?? I do not understand the f(x+y) = f(x)+f(y) thing. Does some point c make f continuous on R??
Proofs. See attached file for full problem description.
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
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 *
Let G be a finite group, let N be a normal subgroup of G, and let x be an element of G. Show that if the order of x in G is relatively prime to |G|/|N|, then x is an element of N. We know that xNx^(-1) is identical to N when N is normal, for any x. Also we know that |G|/|N| is a factor of (or divides) |G|. How to show x i
(a) Let f be analytic in a bounded region D and its boundary C, such that |f(z)| = 1 on C. Show that f has at least one zero inside D, unless f is a constant. (b) Let f(z) be an analytic function in a region D except for one simple pole and assume |f(z)| = 1 on the boundary of D. Prove that every value a with |a| > 1 is take
This question has 3 parts: a) Write a computer program using MATLAB to generate random numbers. Use your program to generate, say, 100,000 random numbers. How long did the computer take to generate the random numbers? Roughly how long does it take for the computer to generate a single random number? b) Using a sample of th
(1) State the definition of equivalence relation.... and (2) Give one example of an abelian group and two (2) examples of nonabelian groups
1. I need a simple definition of a (1) group (2) abelian group (3) nonabelian group 2. Give one example of an abelian group and 2 examples of nonabelian groups.
Let A={-1,0,1,2} , B = {-2,3,4} and C= {-2,0,1,4}. Find: (1) (A U B) ^ C = I used ^ for "intersected with" symbol, U = union (2) (A - B) U C = (3) Give an example that a mapping from A to B that is surjective but not injective.
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
A) Prove that if G and H are Hamiltonian graph, then G x H is Hamiltonian. b) Prove the n-cube Qn n>=2 is Hamiltonian.
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 =