The licensing department issues plates with three letters followed by three digits for cars, and two letters followed by four digits for trucks, except that there are 137 "objectionable" three-letter prefixes that cannot be used. How many vehicles can be licensed?
** Please see the attached file for the complete problem description ** Please prepare a simple and basic MATLAB code for the 2 attached problems. M-file and word documents with comments will help me understand the codes better. Thank you. 3) Write a recursive function computing the sum of cubes of all integers between 1 an
Given any two real numbers x < y, we can find a rational number q such that x < q< y. Hint: you can prove this by using the following statement: for any positive real number x > 0 there exists a positive integer N such that x > 1/N > 0
Develop a loan amortization project using Excel spreadsheets. This can be a car loan or a home mortgage. You will develop two alternative loan schedules using realistic rates and repayment schedules and write up a comparison of your two amortization schedules. This involves two tables and two line graphs displaying the decrease
1) show that if (a_n)^infinity evaluated at n=1, and (b_n)^infinity evaluated at n=1 are equivalent sequences of rationals, then (a_n) ^infinity evaluated at n=1 is a Cauchy sequence if and only if (b_n)^infinity evaluated at n=1 is a Cauchy sequence. 2) Let epsilon >0. Show that if (a_n)^infinity evaluated at n=1 and (b_n)^
Would someone be able to explain to me how we would find antichains and chains of a powerset? For example, if we had the power set of 4 - P([4]) then how would we derive the antichains, and symmetric chains? What about for the power set of [5]? (where [5] is the set of numbers {1,2,3,4,5}. Is there are a general formul
Please help with the following problem. Provide a step by step explanation. Show that given finite sets A_1, A_2,...,A_n, that are pairwise-disjoint, that is A_i intersection A_ j = empty set for all i not equal to j, then their union is a finite set and the cardinality of their union is the sum of the cardinalities of the s
Please help with the following problem. Provide step by step. Show that equality of integers is an equivalence relation, that is show that equality of integers is reflexive, symmetric, and transitive. Recall two integers z=a--b, w=c--d, a, b, c, d belong to N (natural numbers) are equal if and only if a+d=b+c **where a--b
Prove Each Directly. 1. The product of any two even integers is even. Prove by cases, where n is an arbitrary integer and Ixl denotes the absolute value of x. 2. [-x]=[x] (*Brackets are the x's is the absolute value symbol) Give a counterexample to disprove each statement, where P(x) denotes an arbitrary p
Prove the cancellation law for integers: If a, b, c are integers such that ac=bc and c is non zero, then a=b. Hint for proof* use the cancellation law: Let a, b, c be natural numbers such that ac=bc and c is non zero, then a=b Use the trichotomy of integers.
Show that the definition of negation on the integers is well-defined in the sense that if (a----b)=(a'----b'), then -(a----b)= -(a'----b') (so equal integers have equal negations) where a----b is the space of all pairs equivalent to (a,b)
Not every error in a proof is a false statement. Sometimes every line is true, but the lines don't directly follow the previous lines. All that's needed to fix the error is more detail or explanation. Explain where the error is in the following proof and then fix it. Prove: If n^2 is not divisible by 3, then n is not di
I want this attached code to continue,using the last statement which is i have failed to close 'end'.I know Iam missing something,I want it edited and saved in word.the second how I think it shld look like,but its not working
Please formally prove that if a binary operation * on a set X has an identity element e (element of) X , then it must be unique. Please submit response as a PDF or MS Word file. Infinite Thanks.
Let A, B, C be sets. Show that the sets (A^B)^C and A^(BxC) have equal cardinality by constructing an explicit bijection between the two sets. Conclude that (a^b)^c=a^bc for any natural numbers a, b, c. Use a similar argument to also conclude a^b x a^c= a^b+c
Let A and B be sets. Show that A x B and B x A have equal cardinality by constructing an explicit bijection between the two sets. Then use the following proposition to prove that multiplication is commutative. (Let n, m be natural numbers. Then nxm=mxn) Proposition: Cardinal arithmetic a) Let X be a finite set, and let x b
Part I: Set Theory Look up a roulette wheel diagram. The following sets are defined: A = the set of red numbers B = the set of black numbers C = the set of green numbers D = the set of even numbers E = the set of odd numbers F = {1,2,3,4,5,6,7,8,9,10,11,12} From these, determine each of the following: A?B A?D B?C
Let A, B, C be sets and let X be a set containing A, B, C as subsets. Prove that A intersects (B union C)= (A intersects B) union (A intersects C) A union (X relative complement of A)=X and A intersects (X relative complement of A)=empty set X relative complement (A intersects B)=(X relative compliment of A) union (X re
Prove the Euclidean Algorithm: Let n be a natural number, and let q be a positive number. Then there exist natural numbers m, r such that 0 < or = r < q and n=mq+r Show that m and r exist and are also unique. **Fix q and induct on n, and note that you can only use rules of addition
Prepare written answers to the following assignments: Preview Activity 3 (The Sum of the Divisors Function) Let s be the function that associates with each natural number the sum of its distinct natural number factors. For example, s (6) = 1 + 2 + 3 + 6 = 12. 1. Calculate s (k) for each natural number k from 1 thr
Hello, I have another discrete problem I need help on. It says: How many subsets contain 1 or 2 or 3 in the set {1,2,...,20}? So my teacher told me that {1} is a subset, {1,3,4,5,19} would be a subset (i just chose that randomly), {2} would be a subset, {2,5,6,7,20} would be a subset (again, i just chose that at random
Hello, I have a discrete math problem. It states how many solutions (X_1,...,X_6) in the Natural numbers have the equation X_1+ ... + X_6 = 10 So the way my teacher explained it was (10,0,0,0,0,0) would be one choice, (0,10,0,0,0,0) would be another, so basically it would look like this... (10,0,0,0,0,0) (0,10,0,0,0,0
(a) Proof. Let f be onto. Consider any C is a subset of Y. Let y E f(f^-1(C)). Then y=f(x) for some x E F^-1(C). But the fact that x E f^-1(C) implies that f(x) E C. Moreover, f(x)=y. Therefore y E C. Thus we have proved that f(f^-1(C)) is a subset of C. For the converse, consider any c E C. Since f is onto, there exists a
Bob compares his SAT Verbal score of 400 to Marge's ACT Verbal score of 20. "I whupped ya," he exclaims. "My score is 20 times your score!" Although Bob's multiplication is good, his logic is faulty. Exxplain why?
Let A = {a, b, c} and let R be the relation defined on A defined by the following matrix: M=R = [1,0,0; 1,1,0; 0,1,1 (a) Describe R by listing the ordered pairs in R and draw the digraph of this relation. (b) Is this relation a partial order? Explain. If this relation is a partial order, draw its Hasse diagram.
Let X={1,2,3,4,5}, Y={1,2}. Define relation R on g(x) by ARB iff AY =BY *Note: g(x) is the power set of x and R is a equivalence relation (no need to prove this)* a) C={2,3}. List the elements of [C], the equivalence class containing C. b) How many distinct equivalence classes are there? c) Suppose X={1,2,...,n
Please see attached. Thanks
The percentage of homes with digital TV services stood at 5% at the beginning of 1990 (t=0) and was projected to grow linearly so that, at the beginning of 2003 (t=4), the percentage of such homes was 25%. a) Derive an equation of the line passing through the points A(0,5) and B(4,25). b) Using the equation found in part
S=span{x_1, x_2, x_3}, where x_1=(1,1,1,-1)^T, x_2=(2,-1,-1,1)^T, and x_3=(-1,2,2,1)^T. 1) use Gram-Schmidt algorithm to the sequence {x_1,x_2, x_3} to find an orthonormal basis of S 2) use the result above to find the QR factorization of the matrix A=(x_1l x_2l x_3).
On the set Z of integer numbers we are given a binary operation o as follows: n o m = n + m + nm, for any n, m E Z. Prove that this operation is associative, however the pair (Z, o) is not a group.