Search & Filtering
(S∪T)∘R= (S∘R)∪(T∘R).
Draw the directed graph of the relation
R = {(1,1),(1,3),(2,1),(2,3),(2,4),(3,1),(3,2),(4,1)} ,
S = {(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,3),(4,1),(4,3)} ,
Use these graphs to draw the graphs of (a)
𝑅
−
1
&
𝑆
−
- –p → q
- (p → –q) ∨ –q
- p → –(p ∨ q)
- (p ∧ q) ∨ (–p ∨ q)
- [ (p ∧ q) ∨ –p ] ∧ –q
Suppose you randomly select k of the first 2016 positive integers. What is the smallest k that guarantees that at least one pair of the selected integers will sum to 2017?
5. You have 5 different-colored bottles, each with a distinct cap. In how many ways can these caps be put on the bottles such that none of the caps are on the correct bottles? (Assume that all the caps must be on the bottles.)
Given an=an−1−6an−2 where a0=1 a2=5
a.) list the first 10 terms of the sequence
b.) find a closed form(solve the recurrence relations)
Consider the recurrence relation an=4 an−1−4 an−2
Find the general solution to the recurrence relation and the solution when a0=−2 and a1=3.
Find out if the inverse exists for the following, give reasoning behind your answer. If you conclude that the inverse exists then find the B ́ezout coefficients and the inverse of the modulo. [Hint: Example 2 of section 4.4 in the book]
(a) - (3 points) 678 modulo 2970
(b) - (3 points) 137 modulo 2350
Find out if the following numbers are prime numbers, show your work using prime factorization. You may use code to verify your answer but do not put it up as your solution.:
(a) - (3 points) 773
(b) - (3 points) 733
(c) - (3 points) 377
Prove or disprove that there exists exactly two regular graphs
