Discrete Mathematics Answers

a) Let Qi = {qi|x² + q²x +4 = 0, q is an element of N, x is aan element of R}.
Find ⋃∞ i=1 Qi and ⋂∞ i=1 Qi.

Let a relation R = (x, -x)|x^2 = x (mod2x), whereby x element of positive integer. Determine whether R is reflexive, symmetric, anti-symmetric or transitive.

You are getting engaged and your fiancee 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 )mod10 where n =0, 1, 2,...,9 , without being intercepted and decrypted by other countries. Using number theory method:
(a) State the decrypted message.
(b) Determine the decryption key.
(c) Suggest an improvement to the encryption key to increase the encryption strength

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

Use truth table to show the answer.

using laws of logics how to show that
(∼p∧(∼q∧r))∨(q∧r)⋁(p∧r)↔r

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

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.