Discrete Mathematics Answers

Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of these sets with bit strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.

{3, 4, 5}=0011100000

{1, 3, 6, 10} = 1010010001

{2, 3, 4, 7, 8, 9}= ?

If A={1,2,3} , find the relation R={(a, b) ∈ A²|a>b}

Draw the Venn diagrams for each of these combinations of the sets A, B, and C.

A ∩ (B − C)

(A ∩ B) ∪ (A ∩ C)

(A ∩ ) ∪ (A ∩ )

Show that if A, B, and C are sets, then A ∩ B ∩ C = A ∪ B ∪ C

by showing each side is a subset of the other side.

using a membership table.

Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find

A ∩ B ∩ C.

A ∪ B ∪ C.

(A ∪ B) ∩ C.

(A ∩ B) ∪ C.

if R={(1,2),(2,1),(3,1),(2,3)} be a relation defined on A={1,2,3)then transitive closure of R is

Show that if any five numbers from 1 to 8 are chosen, then two of them will add up to 9. 

an=3an−1+n2−3,n≥,a0=1

There are three kinds of people on an island: knights who always tell the truth, knaves who always lie, and spies who can either lie or tell the truth. You encounter three people, A, B, and C. You know one of these people is a knight, one is a knave, and one is a spy. Each of the three people knows the type of person each of other two is. A says “I am the knight,” B says “A is not the knave,” and C says “B is not the knave". Is there a unique solution to determine the knight, the knave, and the spy? If yes, determine who the knight, knave, and spy are.

Let R br a realtion defined from the set A={1,2,3,4} to the set B={2,3,4,5}as a€A, b€B aRb <-> a+b=5

1. What are the orderd pairs in the relation R

2. Represent R with a matrix