3. Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B. a) the set of sophomores taking discrete mathematics in your school b) the set of sophomores at your school who are not taking discrete mathematics c) the set of students at your school who either are sophomores or are taking discrete mathematics d) the set of students at your school who either are not sophomores or are not taking discrete mathematics 4. Let A and B be sets. Prove the commutative laws from Table 1 by showing that a) A U B = BU A. b) A O B= BOA

Q: Suppose that A, B, and C are sets. Prove that if AC B, then AnC C BN C. Disprove that if An C CBn C,…

A:

Q: 12. For all sets A, B, and C, (AUB) - CC (A-C) U (B-C).

A:

Q: 3. Consider the set of numbers S that are multiples of three and larger than 10. Write S in roster…

A: S is the set of numbers multiple of 3 and larger than 10 In roster notation S={ 12 ,15 ,18,21,24…

Q: If f(x)= Jx and g(x)= 2x+5, then state the domain of (gof \x).

A:

Q: Suppose set A={1,2,3,...,50} is divided into exactly two disjoint, nonempty sets. For example, one…

A: My approach is the I break into 2 disjoint part and take cardinality(number of element) of every…

Q: Identify the type of set (finite, infinite or empty) as described by the following: 1. A = {stars in…

A: A set is said to be finite if it contains only finite number of elements. A set is said to be…

Q: Let U be set of letters in the English alphabet, A be the set of distinct letters in the word…

A: Question in 2 is not clear what is True or False.

Q: 5. Write the set {0, 3, 12, 27, 48, 75 ...} in set builder notation

A:

Q: Let A = {1,2,3,4,5,6}, how many different relations are there on a set A?

A: First, we need to know definition  of the Cartesian Product of a set is with itself. The Cartesian…

Q: Define the students enrolled in this class during this semester as a set, S. a. Specify a partition…

A: Let S be the set of students enrolled in this class during this semester. a) Then, consider the…

Q: Draw the Hasse diagram of the given set of A = ({3, 4, 12, 24, 48, 72},/)

A:

Q: Suppose that there are 27 students in discrete mathematics class. Show that the class must have at…

A: Here we solve this question by contradiction.

Q: Which of the following is an empty set? a. set of counting numbers less than 10. b. set of bachelor…

A:

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are  red

Q: For each of the pairs of sets, determine whether the first is a subset of the second, the second is…

A: All elements in the subset must be an element of the set but vice versa is not true.

Q: 3. [8] Let A = {a, b, c} and B = {u, v}. Use the set-roster notation to write the elements in the…

A:

Q: 1. Show that 2 is a primitive root modulo 13. 2. For each element a in T, find the index of a mod 13…

A: T=1,2,3,4,5,6,7,8,9,10,11,12

Q: Draw a diagram out of these sets

A:

Q: Suppose that every student in a discrete mathematics class of 25 students is a freshman, a…

A:

Q: 4. Consider the set N = {a,b,c}

A: Answer well explained above

Q: Create a Venn Diagram to represent the sets A = {b, c, d, e} and B = {a, b, f, g}.

A: The given sets are:

Q: 2. Let A = {a, e, g, i, s}, B = {g, i, m, o, p, y}, and C = {a,b, o, r, t}. Find each of the…

A: Sets:A=a, e, g, i, sB=g, i, m, o, p, yC=a, b, o, r, t