Question: Problem 1 (15 marks) Let S be a set. (a) Show that for any set T and any function f : S > T, the

Problem 1 (15 marks) Let S be a set. (a) Show that for any set T and any function f : S > T, the relation R f Q S x 5, dened as: [3,5') E Rf if and only ifs) =f(s') is an equivalence relation. (9 marks) (b) Show that if R g S x S is an equivalence relation, then there exists a set T and a function f3 : S > T such that: (5,5') E R if and only iffR(s) 2 g (5") (6 marks)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Please Solve all the parts, thanks in Advance Figure 1 : Convex-hull of S {a, b, c, d,e, f} QUESTION 7 (12 Marks) We define a point in the plane as a pair of real numbers (x, y). The aim of this...

QUESTION 7 (12 Marks) We define a point in the plane as a pair of real numbers (x, y). The aim of this question is to estimate a lower bound for any algorithm that computes the convex-hull of a given...

3 problems to solve in jupyter python. it relates to programming and maths. DO NOT USE any file compression method. While the tasks below mention magnetic fields and particle orbits, you do not need...

Problem 5 (40 marks) SPY and XIU are ETFs tracking the S&P 500 and S&P/TSX 60 index, which are often used as proxies for the US and Canadian stock markets, respectively. From a set of their...

[101A_B_1] 1. (15 pts) Let D denote the set of training examples, td denote the true target value of an example din D, where d is represented by feature vector (x1,x2,...,x), and od be the predicted...

Question 3 [15 marks] Let X be a random variable with the Pareto probability density function (pdf) given by fx(x) = r 2 8. 0. where a and / are positive constants. a. Find Fx(x), the cumulative...

Problem 1 (15 marks) (27 minutes) Last night, the sprinkler system at Plant A was accidentally set off. Most of the cost records in Plant A for the month just completed (May) were destroyed. The...

Problem 1 (2 marks). Let f: 1R?Hr > ]R be defined by f(x) 2 xi\" - - 46%\ x}n, where > 0 Problem 1 (2 marks). Let f: Rn + R be defined by f (x) x 1 for all j , n. This function, called Cobb-Douglas,...

6. [15 marks] Let N denote the set of nonnegative integers. Give an example of a function f : N - N such that f(f (n) ) = n + 1 for all n E N or prove that none exists. Hint. Consider f(0)

Problem 1. (15 points) Let N = {0, 1, 2, 3, . . . }. Let N131 be the set of all positive integers whose last three digits are 131. Find a bijection f : N > N131 between these two sets and prove that...

How many bouquets with 7 branches can be made from 5 types of flowers?

You purchased $60,000 worth horizontal milling machine in your ongoing project. You expect to save labour costs by $20,000 in year 1, $45,000 in year 2 and $10,000 in year 3. This machine will have...

To determine the equity value of an entire business, discount the firm's Blank _ _ _ _ _ _ using the Blank _ _ _ _ _ _ as the discount rate, then subtract the value of the firm's Blank _ _ _ _ _ _ .

EcoWave manufactures environmentally friendly packaging made from biodegradable plastics and recycled paper. Jose Gonzalez was recently hired as a the Operations Manager at EcoWave. His goal is to...