Homework Answers
Cartisian product of A and B is
{(1,a),(1,b),(1,c),(2,a),(2,b),(2,c)}
Cartisian product of A, B and C is
{(0,1,0),(0,2,0),(1,1,0),(1,2,0),(0,1,1),(0,2,1),(1,1,1),(1,2,1),(0,1,2),(0,2,2),(1,1,2),(1,2,2)}Add Answer to:
14. Ax B={(a,b)|ae Aabe B} The Cartesian product of the sets, A, A......A. denoted by A,...
do 4,5,6 Let A = {1,2,3) and B = {a,b). 1. Is the ordered pair (3.a)...
do 4,5,6
Let A = {1,2,3) and B = {a,b). 1. Is the ordered pair (3.a) in the Cartesian product Ax B? Explain. 2. Is the ordered pair (3.a) in the Cartesian product A x A? Explain. 3. Is the ordered pair (3, 1) in the Cartesian product A x A? Explain. 4. Use the roster method to specify all the elements of Ax B. (Remember that the elements of Ax B will be ordered pairs. =1'. 5. Use the...
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3}...
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3} n times). (a) What is Sl? Give a brief explanation. (b) For 0 <k <n, let T be the set of all elements of S with exactly k occurrences of 3's. Determine |Tx I, and prove it using a bijection. In your solution, you need to define a set Ax that involves subsets and/or cartesian products with known cardinalities. Then clearly define your bijection...
Set theory Find f(A) and f-(B) for the given function and sets. (a) f : R...
Set theory
Find f(A) and f-(B) for the given function and sets. (a) f : R → R is defined by f(x) = x2 + 1, A = [-1,2], B = [0,4]. (b) f R R is defined by f(x) - sin z, A [0, ], B [0,2]. (c) f : R → Z is defined by f(x)-번 (the floor function), A = (0,4], B-(0,1,2). (d) f : R-(0) → R is defined by f(z) = x + 1, As...
need java code. (d) is cartesian product rule. Design a program to let user enter two...
need java code. (d) is cartesian product rule.
Design a program to let user enter two lists of numbers within the range [0, 9] from keyboard, you could either use flag to denote end of the list or ask user to enter the list size first and then enter the list numbers. Each of these two lists represents a set (keep in mind that duplicate elements are not allowed in a set), so we have two sets A and B....
8. A different way to multiply two square matrices, called the Lie product and denoted A...
8. A different way to multiply two square matrices, called the Lie product and denoted A x B, is defined by A x B = AB - BA 1. (2 pts) Show A x B = -(B x A) 2. (4 pts) Show A ~ (B+C) (A x B) +(AXC) 3. (4 pts) Show Ax(B x C) + B x (C x A) + C (A x B) = 0
1. Prove the following results and give the logical explanation. a. E(aX) = aE (X), where...
1. Prove the following results and give the logical explanation. a. E(aX) = aE (X), where a is a constant. b. E(X + b) = E(X) + b, where b is a constant. You are interested in studying the distribution of the workout days of 100 students. The 2. collected data is summarized in the table below: Workout Days 15 18 20 24 Students Count 10 17 33 20 12 8 Calculate the average number of workout days for students?...
Consider an economy occupied by many households with two types denoted by i, (i- A, B)...
Consider an economy occupied by many households with two types denoted by i, (i- A, B) who are facing the two-period consumption problem. Each household i- A, B is facing the following utility maximization problem: max subject to ci bi(1+r)bo where yl and yẳ are household is exogenous income in period t 1, 2 . CI and då are household i's consumption in period t = 1.2. , bị is household i's bond holdings of which bo is exogenously given,...
2. Consider the linear system Ax = b, where [101] A = 14 1 cil, b=...
2. Consider the linear system Ax = b, where [101] A = 14 1 cil, b= 0, [O_c2 1 x= | and det A = 2 and C1C2 = 3. What is the value of x? A. 1 O Ī la
The 3-Dimensional Matching (3DM) decision problem takes as input three sets \(A, B\), and \(C\), each...
The 3-Dimensional Matching (3DM) decision problem takes as input three sets \(A, B\), and \(C\), each having size \(n\), along with a set \(S\) of triples of the form \((a, b, c)\) where \(a \in A, b \in B\), and \(c \in C\). We assume that \(|S|=m \geq n\). The problem is to decide if there exists a \(3 \mathrm{DM}\) matching, i.e. a subset of \(n\) triples from \(S\) for which each member of \(A \cup B \cup C\) belongs...
There is a natural relationship between sets and bit strings which is called the characteristic vector...
There is a natural relationship between sets and bit strings which is called the characteristic vector for a set. We'll look only at subsets of the universe U = {0, … , n-1} for some n, but the concept can be generalised to arbitrary sets. For a set S C U, the characteristic vector is denoted by xs and is an n-bit string where bit j is 1 if and only if j E S. For example, with n 4...
do 4,5,6
Let A = {1,2,3) and B = {a,b). 1. Is the ordered pair (3.a) in the Cartesian product Ax B? Explain. 2. Is the ordered pair (3.a) in the Cartesian product A x A? Explain. 3. Is the ordered pair (3, 1) in the Cartesian product A x A? Explain. 4. Use the roster method to specify all the elements of Ax B. (Remember that the elements of Ax B will be ordered pairs. =1'. 5. Use the...
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3} n times). (a) What is Sl? Give a brief explanation. (b) For 0 <k <n, let T be the set of all elements of S with exactly k occurrences of 3's. Determine |Tx I, and prove it using a bijection. In your solution, you need to define a set Ax that involves subsets and/or cartesian products with known cardinalities. Then clearly define your bijection...
Set theory
Find f(A) and f-(B) for the given function and sets. (a) f : R → R is defined by f(x) = x2 + 1, A = [-1,2], B = [0,4]. (b) f R R is defined by f(x) - sin z, A [0, ], B [0,2]. (c) f : R → Z is defined by f(x)-번 (the floor function), A = (0,4], B-(0,1,2). (d) f : R-(0) → R is defined by f(z) = x + 1, As...
need java code. (d) is cartesian product rule.
Design a program to let user enter two lists of numbers within the range [0, 9] from keyboard, you could either use flag to denote end of the list or ask user to enter the list size first and then enter the list numbers. Each of these two lists represents a set (keep in mind that duplicate elements are not allowed in a set), so we have two sets A and B....
8. A different way to multiply two square matrices, called the Lie product and denoted A x B, is defined by A x B = AB - BA 1. (2 pts) Show A x B = -(B x A) 2. (4 pts) Show A ~ (B+C) (A x B) +(AXC) 3. (4 pts) Show Ax(B x C) + B x (C x A) + C (A x B) = 0
1. Prove the following results and give the logical explanation. a. E(aX) = aE (X), where a is a constant. b. E(X + b) = E(X) + b, where b is a constant. You are interested in studying the distribution of the workout days of 100 students. The 2. collected data is summarized in the table below: Workout Days 15 18 20 24 Students Count 10 17 33 20 12 8 Calculate the average number of workout days for students?...
Consider an economy occupied by many households with two types denoted by i, (i- A, B) who are facing the two-period consumption problem. Each household i- A, B is facing the following utility maximization problem: max subject to ci bi(1+r)bo where yl and yẳ are household is exogenous income in period t 1, 2 . CI and då are household i's consumption in period t = 1.2. , bị is household i's bond holdings of which bo is exogenously given,...
2. Consider the linear system Ax = b, where [101] A = 14 1 cil, b= 0, [O_c2 1 x= | and det A = 2 and C1C2 = 3. What is the value of x? A. 1 O Ī la
There is a natural relationship between sets and bit strings which is called the characteristic vector for a set. We'll look only at subsets of the universe U = {0, … , n-1} for some n, but the concept can be generalised to arbitrary sets. For a set S C U, the characteristic vector is denoted by xs and is an n-bit string where bit j is 1 if and only if j E S. For example, with n 4...
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