Question 1. Let A and B be sets. (a) Prove that P(A) nP(B) = P(ANB). (b) Prove that P(A) UP(B) ≤ P(AUB). (c) Give an example of sets A, B such that P(A) UP(B) ‡ P(AUB). Question 2. Suppose that A, B and C are sets which satisfy both of the following conditions: (a) AUC BUC; (b) AnCBN C. Prove that A = B. Question 3. Let = be the relation defined on wxw by (a, b) = (c, d) ad = cb. Determine whether or not = is an equivalence relation on wxw. (Of course, it is not enough merely to state that = is an equivalence relation or to state that = is not an equivalence relation. You must justify your answer!) Question 4. Let h: ww be the function defined recursively by h(0): = 1 h(n + 1) = 5h(n) + 7n. Prove by induction that for all new, h(n) = 5n+7n 2

Q: A bag contains five red marbles, four green ones, one lavender one, two yellows, and two orange…

A:

Q: The subject is sets. The question is: What is the relationship between set A and set B if A = {x|x…

A: Set A represents the annual salary that exceeds one million dollars and set B represents players who…

Q: Please help me understand set theory.

A: The set theory is a mathematical theory which includes well-determined collections of…

Q: Can I use symbols other than braces when writing sets using the roster method?

A:

Q: Provide 2 examples of sets with |A| = 4, |B| = 3, |AUB| = 6

A: Number of elements in set A is 4, in set B is 3 and in set A U B is 6.

Q: Consider the set {x|x less than or equal to -3} (in set-builder notation)

A:

Q: May sound like an obvious question but how does the set contain 0 when n is greater than 1?

A:

Q: What properties in Abstract Algebra are true if a set is a subset of a different set?

A: The question is asking about the properties in abstract algebra that hold true when a set is a…

Q: Fill in the Venn diagram with the appropriate numbers based on the following information. n(A) = 32…

A: Given that And the venn- diagram is  we have to find the elements in all regions

Q: Write the following sets in set-builder notation. There may be more than one correct way to do it.…

A:

Q: Hello I am having trouble understanding Set Theory and Subsets.

A: Set theory is dealing with objects that are related to the mathematics and it is also a branch of…

Q: To determine the set indicated below, use A = {18, 19, 20} , B = {18, 19, 20, 23, 26}, and C = {14,…

A: Given that    A= {18, 19, 20} B = {18, 19, 20, 23, 26}  C = {14, 16, 17, 19, 20, 23, 24} The details…

Q: Give an example of a set that contains nine elements of which two are sets. List three Subsets of…

A: Let the set which contains 9 elements be, A=1,2,3,4,5,6,7,8,9

Q: c) Create a set comprehension for the set F = {1,2,4,8 %3D

A: Solution of the problem as follows

Q: Hi, What is the "{}" when it comes to sets? Like for example what is the difference between {x} and…

A: The "{}" means "the collection of" or "a set". There is a big difference in  between {x} and {{x}}.…

Q: define sets.

A: A set is a collection of well defined objects.

Q: Can you explain what the process was to find the cardinality?

A: Cardinality: The cardinality of a set is a measure of the number of elements in the set. For…

Q: What relationship (subset, intersect, disjoint, or equivalent) can be used to characterize the two…

A: Remind that, SUBSET : Any set A is said to be a subset of B if all elements of A are also elements…

Q: A bag contains two red marbles, three green ones, one lavender one, three yellows, and four orange…

A: