MY-ASSIGNMENTEXPERT™可以为您提供lse.ac.uk MA210 Discrete Mathematics离散数学课程的代写代考和辅导服务！
这是伦敦政经学校离散数学课程的代写成功案例。
MA210课程简介
Availability
This course is available on the BSc in Business Mathematics and Statistics, BSc in Data Science, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.
Pre-requisites
MA103 Introduction to Abstract Mathematics, or an equivalent course giving a background in rigorous mathematics.
Prerequisites
Course content
This is a course covering a number of concepts and techniques of discrete mathematics. Topics covered: Counting: selections; inclusion-exclusion; generating functions; recurrence relations. Graph Theory: basic concepts; walks, paths, tours and cycles; trees and forests; colourings. Coding theory: basic concepts; linear codes.
Teaching
This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Lent Term.
MA210 Discrete Mathematics HELP（EXAM HELP， ONLINE TUTOR）
A quasi-Boolean function maps an $n$-tuple $\left(\mathrm{P}0, \mathrm{P}_1, \ldots, \mathrm{P}{n-1}\right)$ of Boolean values to one of three values: $0=$ (False), $0.5=$ (Maybe) or $1=$ (True).
(a) How many different $n$-variable quasi-Boolean functions are there?
(b) If you allow quasi-Boolean $(0,1 / 2,1)$ input as well, How many different $n$ variable functions are there?
(a) For each of the $n$ input variables, there are three possible values: $0$, $0.5$, or $1$. Therefore, there are $3^n$ possible input combinations. For each input combination, there are three possible outputs: $0$, $0.5$, or $1$. Therefore, there are $3^{3^n}$ possible quasi-Boolean functions of $n$ variables.
(b) If we allow quasi-Boolean $(0,1/2,1)$ inputs, then there are still $3^n$ possible input combinations, but now each input can take on one of $2^2=4$ possible values. Therefore, there are $4^n$ possible input combinations. For each input combination, there are still three possible outputs: $0$, $0.5$, or $1$. Therefore, there are $3^{4^n}$ possible quasi-Boolean functions of $n$ variables when we allow quasi-Boolean $(0,1/2,1)$ input values.
Use the laws of Boolean algebra: commutative, associative, distributive, De Morgan’s, etc., and the shorthand $\mathrm{P} \rightarrow \mathrm{Q}$ for $\neg \mathrm{P} \vee \mathrm{Q}$, to prove the following equivalences. (a) $\mathrm{P} \rightarrow(\mathrm{Q} \rightarrow \mathrm{R}) \equiv(\mathrm{P} \wedge \mathrm{Q}) \rightarrow \mathrm{R}$ (b) $(\mathrm{P} \wedge \mathrm{Q}) \rightarrow \mathrm{R} \equiv(\mathrm{P} \rightarrow \mathrm{R}) \vee(\mathrm{Q} \rightarrow \mathrm{R})$
(a) We can start with the left-hand side:
$$
\begin{aligned}
\mathrm{P} \rightarrow(\mathrm{Q} \rightarrow \mathrm{R}) & \equiv \neg \mathrm{P} \vee(\neg \mathrm{Q} \vee \mathrm{R}) & & \text { definition of implication } \
& \equiv(\neg \mathrm{P} \vee \neg \mathrm{Q}) \vee \mathrm{R} & & \text { associativity of } \vee \
& \equiv \neg(\mathrm{P} \wedge \mathrm{Q}) \vee \mathrm{R} & & \text { De Morgan’s law } \
& \equiv(\mathrm{P} \wedge \mathrm{Q}) \rightarrow \mathrm{R} & & \text { definition of implication }
\end{aligned}
$$
Therefore, $\$ \backslash$ mathrm ${P} \backslash$ rightarrow $(\backslash$ mathrm ${Q} \backslash$ rightarrow $\backslash$ mathrm ${R})$ lequiv $($ mathrm ${P} \backslash$ wedge $\backslash$ mathrm ${Q}) \backslash$ rightarrow $\backslash$ mathrm ${R} \$$.
(b) We can start with the left-hand side:
$$
\begin{aligned}
(\mathrm{P} \wedge \mathrm{Q}) \rightarrow \mathrm{R} & \equiv \neg(\mathrm{P} \wedge \mathrm{Q}) \vee \mathrm{R} & & \text { definition of implication } \
& \equiv(\neg \mathrm{P} \vee \neg \mathrm{Q}) \vee \mathrm{R} & & \text { De Morgan’s law } \
& \equiv(\mathrm{P} \rightarrow \mathrm{R}) \vee(\mathrm{Q} \rightarrow \mathrm{R}) & & \text { definition of implication }
\end{aligned}
$$
Therefore, $\$ \backslash \backslash$ mathrm ${P} \backslash$ wedge $\backslash$ mathrm ${Q}) \backslash$ rightarrow $\backslash$ mathrm ${R}$ $\backslash$ lequiv $\backslash$ mathrm ${P} \backslash$ rightarrow $\backslash$ mathrm ${R}) \backslash$ vee $($ mathrm ${Q} \backslash$ rightarrow $\backslash$ Imathrm ${R}) \$$.
MY-ASSIGNMENTEXPERT™可以为您提供LSE.AC.UK MA210 DISCRETE MATHEMATICS离散数学课程的代写代考和辅导服务！
