Discrete Mathematics Answers

Alice decides to set up an RSA public key encryption using the two primes p= 31 and p= 41 and the encryption key e= 11.You must show all calculations, including MOD-calculations using the division algorithm!
Bob decides to send the message M= 30to her using this encryption. What is the code C that he will send her?
What is Alice’s decryption key d?
Alice also receives the message C= 101from Carla. What was her original message M?

In an engineering class there are 15 students taking chemistry,20 students taking mathematics. Of these students,10 are taking both chemistry and mathematics.How many students are taking either chemistry or mathematics?

Make negation of the following statements.
I4) All students have taken a course in mathematics.
15) Some students are intelligent, but not hardworking.

Five different colored flags can be hung in a row to make a coded
signal. How many signals can be made if a signal consists of the display of one
or more flags?
A. 11
B. 13
C. 15
D. 17

A keyboard has its keys removed. If the last line of the letters were
jumbled, how many ways can I rearrange it so that consecutive letters
are beside each other?
A.120
B. 144
C. 156
D.196

A palindrome number is a number that is read similarly backwards. How
many possible 5-digit palindromic numbers are there?
A. 608
B. 648
C. 688
D. 728

∀x∃y(x + y = 2 ∧ 2x − y =1

6. Use truth tables to determine whether the argument form is valid. [5 Marks]
a. There is an undeclared variable or there is a syntax error in the first five lines.
b. If there is a syntax error in the first five lines, then there is a missing semicolon
c. There is not a missing semicolon

The generating function of the sequence {1,2,3...n..} is (1-z)².

Analyse the operations, using illustration, if two network shortest path algorithm, providing an example of each