Discrete Mathematics Answers

Imagine you own two shops selling cakes. You are tracking the number of cakes sold

in each shop each day over a ten day period. Each cake in Shop 1 makes 3 dollars profit. Each cake in Shop 2 makes 4 dollars profit.

The following arrays contain the cakes sold in each shop over the 10 consecutive days.

shop1=[4, 5, 3, 6, 0, 5, 5, 6, 4, 5]

shop2=[5, 3, 1, 1, 3, 5, 3, 6, 3, 3]

Write a MATLAB program that computes the running profit of each shop and displays one of

the following messages (whichever applies) after each round n for n = 1, 2, . . . , 10:

Shop 1 is leading

Shop 2 is leading

It is a tie

[Hint: You should use an if construct.]

Also, at the end of your program, use the find command to identify (and display) the rounds in which the number of sales (not profit) were the same for the two shops, and use the length command to compute (and display) the number of such days. Include appropriate headings in your output.

Build a truth table then verify if the proposition is Tautology, Contradiction, and Contingency.

(p ↔ q ) Λ ( ┐p Λ q )    

. Which of the intervals (0, 5), (0, 5], [0, 5), [0, 5], (1, 4], [2, 3], (2, 3) contains

a) 0?

b) 1?

c) 2?

d) 3?

e) 4?

f ) 5?

Use mathematical induction to prove that 2n > n2 , for n > 5 .

Find, showing all working, a recursive definition of the sequence with general term

t_n = 6 (n + 1)!/3ⁿ, n >= 1

Prove that for any integer n

n, if n

n is an odd integer, then 6n

2

+5n+1

6n2+5n+1 is an even integer.

A bank password consists of two letters of the English alphabet followed by two digits. How many different passwords are there?