(a) For U = {1, 2, 3}, let A = P(U). Define the relation R on A...

Question:

(a) For U = {1, 2, 3}, let A = P(U). Define the relation R on A by B R C if B ⊆ C. How many ordered pairs are there in the relation R?
(b) Answer part (a) for U = {1, 2, 3, 4}.
(c) Generalize the results of parts (a) and (b).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jun 21, 2016 08:34 AM

See More Questions

Let n Z+ with n > 1, and let A be the set of positive integer divisors of n. Define the relation R on A by x R y if x (exactly) divides y. Determine how many ordered pairs are in the relation R when...
(a) Let f: AB, where |A| = 25, B = {x, y, z}, and | f-l(x) | = 10, | f-l(y) | = 10, |f-1(z)| = 5. If we define the relation R on A by a R b if a, b A and f(a) = f(b), how many ordered pairs are...
For X = {0, 1}, let A = X X. Define the relation R on A by (a, b) R (c, d) if (i) a < c; or (ii) a = c and b d. (a) Prove that R is a partial order for A. (b) Determine all minimal and maximal...
After pollen lands on a stigma, it is far away from the ovule with the megagametophyte, which holds the egg (the megagamete). How are the two sperm cells transported from the stigma to the egg?
Discuss why single-sourcing is attractive to some companies.
Using the matrix iteration method, how do you find the intermediate natural frequencies?
Find a successful entrepreneurial firm in your community and attempt to chart its development plan. Recognize what methods of growth they have employed.
Copa Company, a manufacturer of stereo systems, started its production in October 2010. For the preceding 3 years Copa had been a retailer of stereo systems. After a thorough survey of stereo system...
What personal experiences or cultural influences have shaped your perspective on aggression and violence, and how have these experiences or influences affected beliefs and attitudes about these...
Tory Enterprises pays $238,400 for equipment that will last five years and have a $43,600 salvage value . By using the equipment in its operations for five years, the company expects to earn $88,500...
Let U denote the set of all points in and on the unit square shown in Fig. 7.29. That is, U = {(x, y) | 0 x 1, 0 y 1}. Define the relation R on U by (a, b) R (c, d) if (1) (a, b) = (c, d), or (2)...
For n Z+, let U = {1, 2, 3, ... , n}. Define the relation R on P(U) by A R B if A B and B A. How many ordered pairs are there in this relation?
A continuous distillation unit, consisting of a perforated-tray column together with a partial reboiler and a total condenser, is to be designed to operate at atmospheric pressure to separate ethanol...
Consider the first-order RL circuit shown in Figure 6.25. a. Derive the input-output differential equation relating $i_{\mathrm{L}}$ and $v_{\mathrm{a}}$. b. Determine the transfer function...
Design a program that has a two-dimensional integer array with 7 rows and 7 columns. The program should store a random number in each element. Then, the program should search the array for saddle...
Find $R_{13}$ and $R_{32}$ for the voltage divider shown in Figure 6.76 so that the current is limited to $2 \mathrm{~A}$ when $v_{i}=110 \mathrm{~V}$ and $v_{\mathrm{o}}=100 \mathrm{~V}$....
Lets say you work in Illinois, and you want to figure out how much income tax you need to pay for the year. Here is what you know: Your hourly wage is $10. You have worked 1000 hours for the year ...
Ahson Tariq is director of operations for CTC. CTC specializes in global merchandising of the world's finest cotton fibers. It is common practice for CTC to purchase cotton in bulk from regional...
Evaluate the definite integral. /3 Jw/6 (4 secy) dy
In the synthesis of the keto acid just given, the dicarboxylic acid decarboxylates in a specific way; it gives Explain. HO rather than HO
Write out the addition and multiplication tables for Zs.
Perform the indicated calculations. a. 2 + 2 + 2 in Z3 b. 2 2 2 in Z3 c. 2(2 + 1 + 2) in Z3 d. 3 + 1 + 2 + 3 in Z4 e. 2 3 2 in Z4
If the vectors in Exercise 3 are translated so that their heads are at the point (3, 2, 1), find the points that correspond to their tails. In exercise 3 (a) a = [0, 2, 0] (b) b = [3, 2, l] (c) c =...
How does the blurring of boundaries between work and personal life in a remote work environment impact employee stress levels, productivity, absenteeism, turnover rates, and organizational stability...
Police Officers Tough and Tricky were investigating the disappearance of Vai, a 10 year-old girl, on her way home from school on a Tuesday. A friend of Vai's said she saw Vai get into a truck but was...
Reflect on transformational and servant leadership style and application of the standards and how it can impact recruitment and retention of qualified special education teachers and staff.

(a) For U = {1, 2, 3}, let A = P(U). Define the relation R on A...

Question:

Step by Step Answer:

a If C U then 0 C 3 For 0 k 3 there are subsets C of U where C k each ...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Linear Algebra questions