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Determine whether each statement is true or false. For each true statement, give a direct evidence as justication. For each false statement, give a counterexample as defense.( separate calculation)
i) If x + y is an even integer, then x and y are both even integers.
ii) If $x^{2} = y^{2}$ , then x=y.
iii) The $m e a n^{1}$ of two even numbers is even.
iv) If x and y are even integers, then x + y is an even integer.

Chardonnay Felix 2021-08-03

Use symbols to write the logical form of the following arguments. If valid, identify the rule of inference that guarantees its validity. Otherwise, state whether the converse or the inverse error has been made.
If you study hard for your discrete math final you will get an A.
Jane got an A on her discrete math final.
Therefore, Jane must have studied hard.

Tabansi 2021-08-02

Express the following in set-builder notation:
a)The set A of natural numbers divisible by 3.
b)The set B of pairs (a,b) of real numbers such that a + b is an integer.
c)The open interval C = (—2,2).
d)The set D of 20 element subsets of N.

pedzenekO 2021-08-02

Let $S = {10 n - 1 : n \in Z}$ , T be the set of odd integers, and $U = {6 m + 4 : m \in Z}$
Prove that discrete math $S \subseteq T \cap U$ .

Dottie Parra 2021-08-02

Suppose that A is the set of sophomores at your school and B is the set of students taking discrete mathematics at your school. Express each of these sets in terms of A and B.
a) the set of sophomores taking discrete mathematics in your school
b) the set of sophomores at your school who are not taking discrete mathematics
c) the set of students at your school who either are sophomores or are taking discrete mathematics
Use these symbols: $\cap \cup$

Kaycee Roche 2021-08-02

Using cardinatility of sets in discrete mathematics the value of N is real numbers
Currently using elements of discrete mathematics by Richard Hammack chapter 18
Let A be a collection of sets such that $X \in A$ if and only if $X \subset N$ and $| X | = n$ for some $n \in N$
Prove that $| A | = | N | .$

tinfoQ 2021-08-01

Prove: Any postage of 24 or more can be constructed using 5 and 7 cent stamps.
Use K and $K + 1$ for the induction hypothesis.

Jaden Easton 2021-08-01

Discrete Math Cryptography
Dan uses the RSA cryptosystem to allow people to send him ecrypted messages. He selects the parameters:
p = 17. q = 41. e = 61. d = 21
What ate the numbers that Dan publishes as the public key?

sanuluy 2021-07-31

Find the SPI form of the Boolean expression whose Karnaugh map is below.
$\begin{array}{cc} y z & y \overset{―}{z} & \overset{―}{y} \overset{―}{z} & \overset{―}{y} z \\ w z & 1 & 1 & 1 \\ w \overset{―}{x} & 1 & 1 & 1 \\ \overset{―}{w} \overset{―}{x} & 1 & 1 & 1 \\ \overset{―}{w} x & 1 & 1 & 1 \end{array}$

snowlovelydayM 2021-07-31

Determine the truth value using truth table (Attach your answer, any image file format):
$p \lor (q \land r) \equiv (p \lor q) \land (u r c or \neq r p \lor r)$

babeeb0oL 2021-07-30

Solve the following recurrence relation:
a) $a_{n + 1} = d a_{n} + c, a_{0} = 0$
b) $a_{n + 1}^{3} = 2 a_{n}^{3}, a_{0} = 5$
c) $F_{n} = 5 F_{n - 1} - 6 F_{n - 2}, F_{0} = 1$ and $F_{1} = 4$

abondantQ 2021-07-30

Let R be the relation from X={1,2,3,5} to Y={0,3,4,9} defined by xRy if and only if $x^{2} = y$

Burhan Hopper 2021-07-30

Find the shortest path from vertex v to vertex w in the graph
each step show your work and label new vertices

permaneceerc 2021-07-30

Consider a relation R on Z — {0} defined by the rule that (z,y) $\in$ R if and only if xy > 0. a) Prove that R is an equivalence relation. b) Determine all elements in the equivalence class containing 1. How many distinct equivalence classes are there?

ddaeeric 2021-07-30

Prove that discrete math by induction that for all integers $n \geq 1$
$\sum_{i = 1}^{n} i^{2} = \frac{n (n + 1) (2 n + 1)}{6}$

Josalynn 2021-07-28

Prove the following fact by induction: Fol all $n \geq 1, 4^{n} \geq 3^{n} + n^{2}$

Lewis Harvey 2021-07-28

Let A, B, and C be sets. Show that $(A - B) - C = (A - C) - (B - C)$

Dolly Robinson 2021-07-22

Solve the traveling salsman roblem for this graph by finding the total weight of all circuits and determining a circuit with minimum total weight

EunoR 2021-07-22

a)Let $A = {1, 2, 3, 4, 5, 6}, A_{1} = {1, 2}, A_{2} = {3, 4} and A_{3} = {5, 6} . I s {A_{1}, A_{2}, A_{3}}$ a partition of A?
b) Let Z be the set of all integers and let:
$T_{0} = {n \in Z ∣ n = 3 k, for some integer k}$
$T_{1} = {n \in Z ∣ n = 3 k + 1, for some integer k}$ ,and
$T_{2} = {n \in Z ∣ n = 3 k + 2, for some integer k}$
Is ${T_{0}, T_{1}, T_{2}}$ a partition of Z?

Bevan Mcdonald 2021-07-21

Given proposontial variables. Tranlate the following sentences into propositional logic

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