Discrete Mathematics Answers

You are getting engaged and your fiancée has hidden the engagement ring. If only one
statement is true, determine which statement is true? Where is the ring?
Statement 1: The ring is in this box --->A
Statement 2: The ring is not in this box --->B
Statement 3: The ring is not in box A --->C

Suppose that you need to deliver the message “161803398” which is the pass key for a weapon
activation to country X. Encrypt the message using Caesar cipher with the encryption key,
(n + 2^2 )mod9 where n =1, 2,...,9 , without being intercepted and decrypted by other countries.
(a) State the decrypted message.
(b) Determine the decryption key.
(c) Suggest an improvement to the encryption key to increase the encryption strength.

Which of the following binary relations is true a ∧ b :
Function / invective / surjective / total / symmetrical / reflexive / transitive

define Q(q): for all value of p in N, where p<q such that NOT(there exist k in N, where (q=k*p)^(k<q))
Concisely, for which numbers q in N, when Q(q) is true?

Draw the truth tables of Conjunction, disjunction and Biconditional
statements.

Write the set M = {1/3, 1/2, 3/5, 2/3, 5/7 ........} In the set builder form.

A panel is conducting an interview on six candidates of different heights. If they are to put them in line, in how many ways can they arrange them in line such that no three consecutive candidates are in increasing order of height from front to back?

1. If a quiz contains five multiple-choice questions, each of which has 4 choices. In how many ways can this be answered?
2. How many different ways can a visiting nurse see six patients if she is to visit at most 3 of them in one day?
3. How many different signals using 9 flags can be made if 4 are red, 3 are blue and 2 are white?
4. In how many ways can 5 individuals be seated in a round table with 5 chairs if 2 of them refuse to sit next to each other?
5. If a basketball team has 10 games to play, how many different outcomes of 6 wins and 4 losses are possible?
6.There are 12 people at a party. If they all shake hands once, how many different handshakes are there?
7. In how many ways can 6 individuals be seated in a row if three insist on sitting next to each other?

Draw both the NAND and NOR implementations of the below functions.

1) F(x,y,z)= x’y’ + xz’ + yz

2) G(x,y,z) = (x’+ y) (x + z) (y’+ z)

A panel is conducting an interview on six candidates of different heights. If they are to put them in line, in how many ways can they arrange them in line such that no three consecutive candidates are in increasing order of height from front to back?