# Recently Submitted Homework Problems: discrete math

248. Spam e-mail containing a virus is sent to 1000 email addresses. After 1 second, a recipient machine broadcasts 10 new spam e-mails containing the virus, after which the virus disables itself on that machine. How many e-mail are sent at then end of 20 seconds?(Answered)251. Solve the recurrence relation subject to the basis step.

Spam e-mail containing a virus is sent to 1000 email addresses. After 1 second, a recipient machine broadcasts 10 new spam e-mails containing the virus, after which the virus disables itself on that machine. How many e-mail are sent at then end of 20 seconds?(Answered)

254. Prove that the number of binary strings of length n with no two consecutive 0s is given by the Fibonacci sequence term F (n+2).(Answered)

258. What is the cardinality of the following set.

P(S) stands for power set.

Find p (p ((S) for S = {a, b}(Answered)

431. Let A = {1,2,3,4,5}

Which of the following sets of ordered pairs represent functions in A?

1. {(1,1),(2,4),(3,4),(4,5),(5,5)}

2. {(1,4),(2,4),(2,5),(3,4),(4,4),(5,4)}(Answered)

417. A colony of bats is counted every two months. The first four counts are 1200, 1800, 2700, and 4050.

If this growth rate continues, (4 points)

1. What is the recurrence relation of the bat population? (2 points)

2. How many bats are there at the 12th count? Show all work. (Hint: solve the recurrence relation above)

(Answered)

418. Find the minimum number of students needed to guarantee that 4 of them were born (3 points): hint use pigeonhole principle.

1. on the same day of the week (1 point);

2. in the same month.(1 point)

3. Which counting principle applies to the questions above?(1 point)

(Answered)

1569. Determine whether each function is one-to-one, onto, or both. Prove your answer. f(n) =[n/2](Answered)

2028. Can you please help me construct a circuit for a Boolean expression? (Answered)

2521. A club has 6 members: a, b, c, d, e, and f. In how many ways can 3 members be selected to go for a good Indian meal if b and c either both have to go, or neither of them goes?(Answered)

3478. It was proven during the previous lecture that

1+2+3+....+n=[n(n+1)]/2.

Using that result, find the sum of all 3-digit palindromes: a palindrome is a number that can be written as ABA, where 1=(Answered)

5402. answer 4 discrete problems

(Answered)