Let S be the set S={a,b,c}. 1. Write all the elements of the power set of S: the set of all subsets of S. 2. Subset relation defines a partial order R on the power set of S. That is, for two subsets A and B: (A, B) ∈? if and only if A⊆?. Describe this partial order using ordered pairs or a hierarchy diagram. 3. Find the largest subset of the power set of S such that the relation R is a total order on that set.

Let S be the set S={a,b,c}. 1. Write all the elements of the power set of S: the set of all subsets of S. 2. Subset relation defines a partial order R on the power set of S. That is, for two subsets A and B: (A, B) ∈? if and only if A⊆?. Describe this partial order using ordered pairs or a hierarchy diagram. 3. Find the largest subset of the power set of S such that the relation R is a total order on that set.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Determine the number of distinct subsets for the given set {t, a, p, e, f, g}.
Needs explaination
4. Check if the following relations are partial order, or equivalence, or none. For the equivalence relations, find equivalence classes and par- tition, for partial orders, draw a Hasse diagram. (i) A= {a, b, c, d, e, f}, RA = {[a, a], [b, b], [c, c], [d, d], [e, e], [f, f], [c, d], [f, c], [d, f], [c, f], [d, c], [f, d]}, (ii) B={a, b, c, d, e, f}, RB={[a, a], [b, b], [c, c], [d, d], [e, e], [f, ƒ], [c, a], [b, a], [b, f], [c, d], [c, b], [a, d, f, d], [c, f}.
Consider the "divides" relation on the set A = {1, 2, 3, 5, 6, 7,8, 10, 20, 30, 60, 70} (a) Draw the Hasse Diagram for this poset. (b) Find the maximal elements or explain why there are no maximal elements. |(c) Find the minimal elements or explain why there are no minimal elements |(d) Find the greatest element or explain why there is no greatest element. (e) Find the least element or explain why there is no least element.
Draw the Hasse diagram for the following partial order.
Find the indicated sets with A, B, and U defined below. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) U = {1,2,3,4,5,6,7,8,9,10}A = {1,2,3,4,5}B = {4,5,6,7}C = {5,6,7,8,9,10} (a) A ∩ (B ∪ C)= { }(b) A ∩ (BC ∪ C) = { }
Let R = {(a, a),(a, b), (b, b), (a, c), (c, c)} be a partial order relation on Σ = {a,b,c}. Let be the corresponding lexicographic order on Σ*, the set of all finite strings over Σ. Which of the following is true? Select one: O a. abbac abb O b. abbac O c. O d. abbac abbaqc O e. abbaaacc abbaab be ba abbab
Choose the answer
Let A be the set of letters in the English alphabet with the usual order. Define (A², <) such that (a, 3) ≤ (7,5) if either a <%, or a = y and 3 ≤ 6. Show that this is a total ordering and also a well-ordering. Use this to justify that the set of words in a particular dictionary is well-ordered. (You may use a, 3, 7, 6, 6, w.)
12 ! Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the set (a, b, c, d). How many relations are there on the set that contain the pair (a, a)?
Part 2. Each relation given below is a partial order. Draw the Hasse diagram for the partial order. (a) The domain is {3, 5, 6, 7, 10, 14, 20, 30, 60}. x ≤ y if x evenly divides y. 1 (b) The domain is {a, b, c, d, e, f}. The relation is the set: {(b, e), (b, d), (c, a), (c, f), (a, f), (a, a), (b, b), (c, c), (d, d), (e, e), (ƒ, f)}
Let A = {3, 4, 5} and B = {5, 6, 7}, and let S be the "divides" relation from A to B. That is, for every ordered pair (x, y) E Ax B, x Sy x|y. Which ordered pairs are in S and which are in S-? (Enter your answers in set-roster notation.) {1} S = %3D S-1