Rewrite the following using mathematical symbols: (a) A is equal to the set whose elements are a, b, and c. (b) The set containing only 1 and 3 is not a subset of the set { 1, 4, 5, 6, 7 } (c) The empty set does not contain 0 as an element.

Q: Write down all elements of {I, J, K} x {W, X}. (Enter your answer in set notation.)…

A: The given problem is to find the Cartesian product of the given sets {I,J,K} and {W,X}.

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: 6. The sets A and B are defined as: A = {2, 5, 7} B = {*, +} (a) Express the set A x B in roster…

A:

Q: Write each set using set-builder notation and inequalities. (a)     A = {1, 2, 3, 4, 5, 6,....}…

A: (a) Given set is A=1,2,3,4,5,6,.... The set-builder notation of set A is given by A=x:x∈N   (b)…

Q: Let A = {1, 3, 5, 7, 9), B = {3, 6, 9), and C = (2, 4, 6, 8). Find each of the following. (Express…

A: Given sets: A=1,3,5,7,9 B=3,6,9 C=2,4,6,8 Find: a) A∪B b) A∩B c) A∪C d) A∩C e) A-B f) B-A g) B∪C h)…

Q: Use an algebraic proof to show that for all sets X ,Y and Z : (X – Y)n ZC = x – (Y u Z) Do not…

A:

Q: Let A, B, and C be sets. Is the following equality true or false? A x (BUC) = (A × B) U (A × C')

A: Sets, distributive law

Q: Which is an example of disjoint sets?   A={multiples of two} and B = {multiples of three}   E =…

A: A={multiples of two} and B = {multiples of three} AnB = {6,12,18,...} = non-empty set E =…

Q: 4. Let A and B be sets. (a) If A and B are subsets of the same universal set U (so A × B is a subset…

A: The definition of complement is given at the end of proof

Q: Give a real-world example of the inclusion/exclusion principle that involves at least two finite…

A:

Q: For all sets A, B, and C, prove that (AUB) - (CA) = AU (B-C) Please indicate the reason for each of…

A:

Q: A = {−1,0,1,2,3}, B = {12,1,4}, C = {x|0 < x ≤ 2}, D = (−1,1]. Find each of the following sets: 6.…

A:

Q: Use the results from parts (a) and (b) to answer part (c). Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9), A =…

A:

Q: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.) {x |  9 − x…

A: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.) {x | 9 − x =…

Q: Prove or disprove: For all sets A,B and C: (A-B)-C = A-(BUC).

A:

Q: Find the intersection of the sets. {a, b, c, d}∩∅

A: Given sets are {a, b, c, d} and an empty set ϕ

Q: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.) {x | 4 − x =…

A: Given: Given set is  x|4-x=9 and x is an integer We want to list the elements of the set in roster…

Q: Prove for every two sets A and B that A∪B= (A-B)∪(B-A)∪(A∩B)

A:

Q: Determine the set of all integers x satisfying the following equations. Express your answers in…

A: Consider the given information. (a) Consider the given equation. 7x≡109 Now, apply the Euclidean…

Q: How do i approach the following question?  Let A and B be sets. Prove that A ∪ B = A ∩ B if and…

A:

Q: Describe each of the following sets by listing its elements (you must use set notation like {a, b}):…

A:

Q: A universal set U with 48 elements has been partitioned into three subsets, A, B, and C. If B is 5…

A:

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

A:

Q: Let the domain be the set of all people. Let: P(x,y): x knows y. Which of the following is the…

A:

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: First we write U in roster form.

Q: Find the complement of the set given that U={x xEI and -3<x<9}. (Enter your answers as a…

A:

Q: Write each set described below using set notation: (a) The set consisting of all odd integers…

A: We have to write each set described below using set notation:(a) The set consisting of all odd…

Q: Specify the sets by roster:    (a) {odd counting numbers less than 11}     (b) {positive multiples…

A: we will find the roster form.