a) If A and B are each countable sets, show that AUB is countable. (Hint: For each set, consider a sequence of all elements, and show how to splice the sequences together to make one sequence. Remember that the sets need not be disjoint.) b) Prove that the union of countably many finite sets is either countable or finite.

Q: Which of the following sets are close under MULTIPLICATION? Choose ALL that apply. I. The set of…

A:

Q: Let J={1,2,3,…}, the set of counting numbers and let R be the set of real numbers. Is R-J countable?…

A:

Q: Show that 2N, the collection of all sets of natural numbers, is uncountable.

A:

Q: An ice cream shop provides the following types of add-ons: hot fudge, caramel, cherry, Reddi-whip,…

A: Consider the  add-ons ice-cream shop provides: Hot fudge,caramel,cherry,redid-whip,chopped…

Q: Which of the following sets are closed? Choose ALL that apply. Show the steps. I. The set of…

A:

Q: Select the set that is equivalent to (Cn B) UA. (Cn B)UA (CUB) UA (CnB) nA (CUB) NA

A:

Q: Use A= {5, 6, 7, 8, 9} and B= {1, 7, 8, 9} to find the set AN B. ANB= (Use a comma to separate…

A:

Q: The diagram below shows ten circles joined by five lines with three circles Place all the…

A: Requirements: Numbers should range from 1 to 10.   Every line has three circles.   3. The amount for…

Q: Identify each condition as (1) Intersecting, (2) Subset, or (3) Mutually Exclusive. Refer to the…

A: A pack of card has 52 cards of which 26 are red in colour and 26 are black in colour. 13 Diamond…

Q: List the set in roster form. C=​{z​| z is an odd integer greater than 21 and less than or equal to…

A:

Q: If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, find the following. (Enter your answers as a…

A:

Q: Express the set using the roster method. the set of natural numbers less than or equal to 6.

A: Given: the set of natural numbers less than or equal to 6. To express: The given set in roster…

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: Show that the set is infinite by placing it in a one-to-one correspondence with a proper subset of…

A:

Q: b. How many elements are in the set {a, {a, b}, {a} }? C. For each positive integer x, let A1` =…

A: Use the definition of set and its elements to solve this problem as in next step.

Q: Determine whether each statement below is true forn = 1, 2, and 3. Enter a comma-separated list of…

A:

Q: Suppose we have a set A={1, 2, 3, 4, 5, 6}. What is the partition of A into three parts? Make sure…

A: We can partition of set A as below

Q: Q17D. Define the sets A, B, C, and D as shown. Find (An C) U (B n D). A C C

A:

Q: Write the set using roster notation: {xIx ∈N and x >24} a. {xIx is a natural number less than 24}…

A: We can write the set in roaster form as below

Q: Assume that in a university with 1000 students, 200 students are taking a course in mathematics, 300…

A:

Q: How many elements does the successor of a set with n elements have?

A: Successor of the set, A is formed by adding an element {A} to the set. So, successor of A will be A…

Q: Rewrite the following using mathematical symbols: (a) A is equal to the set whose elements are a, b,…

A: The elements of a set are always presented using curly braces. If P is a subset of Q, then it can be…

Q: (a) Set-builder form: x x is a natural number and x>5} Roster form:| (b) Roster form: {15,16,17}…

A:

Q: Give an example that achieves the following two infinite sets A and B with A C B and A - B.

A:

Q: Identify the set shown below as finite or infinite, {10, 11, 12, ..., 40} ..... OInfinite O Finite

A:

Q: Write an element from the set B × A × C

A: