Computer Theory: Truth Tables, Logic, Automation, and Sets Analysis

This computer theory assignment delves into several key concepts. It begins with an explanation of truth tables, their construction, and their use in propositional calculus and Boolean algebra. The assignment then explores logical equivalence, contrapositive statements, and contradictions, providing examples for clarity. It further examines brute-force attacks, discussing how they work, the tools used, and methods to prevent them. The assignment then transitions to automation, defining it and exploring its applications, including state machines and their components. Finally, it explains the Cartesian product of sets and regular languages within the context of automata theory. The assignment provides a comprehensive overview of these fundamental computer science topics.

Running head: COMPUTER THEORY BASICS
COMPUTER THEORY BASICS
Name of the student:
Name of the university:
Author Note:

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Table of Contents
Answer 1:...................................................................................................................................2
Answer 2:...................................................................................................................................3
Answer 3:...................................................................................................................................4
Answer 4:...................................................................................................................................5
Answer 5:...................................................................................................................................6
References..................................................................................................................................7

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Answer 1:
A truth table is a tabular representation of the truth values of propositional variables
and compound propositions. It is used in logic; particularly in propositional calculus, Boolean
algebra, and Boolean functions. It is a breakdown of all possible truth value outcomes a given
compound proposition can attain. Such outcomes are based on all possible truth value
combinations of the propositional variables that make up the given compound proposition,
hence the name truth table.
A truth table usually contains multiple rows and columns. The table has one column
for each propositional variable; p, and q for example. The number of rows of the truth table is
determined by the number of propositional variables that make up the compound proposition
(Geuvers and Hurkens 2017). The number of rows is equal to 2 to the power of the number
prepositional variables. For instance, if we had three propositions p, q, and r, there would be
8 rows. This is done to guarantee that there are enough rows to cover all possible truth value
combinations. Each row of the truth table contains one possible combination of the truth
values of propositional variables; for instance, T(p)=0, T(q)=1, and T(r)=0. The resulting
truth value of the final compound proposition that is based on these true values is represented
at the end of the same row.
A truth table can be used as a way of organizing complex compound propositions, and
list out the outcome of all possible scenarios. Furthermore, truth tables are used to check if a
certain compound proposition is either a tautology, or consistent, or a contradiction (Button
2016). Truth tables may also be used to check whether or not two compound propositions are
equivalent; based on the outcome of their respective truth tables. Moreover, in Boolean

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algebra, truth tables can be used to reduce basic Boolean operations to simple correlations of
inputs and outputs without need for logic gates or code. For example, an adder for binary
addition can be represented with a truth table. Additionally, truth tables synergize with
Boolean algebra; where both are used by engineers to produce the simplest possible circuit
that will perform desired logic function. Which improves efficiency and cuts costs.
Answer 2:
In the branch of mathematics, logic is applied to derive truths from the statements.
When certain statements are given, the equivalent logical statements are constructed that
states the same truth as highlighted in the given statements. The first statement that is already
given is considered as a fact. The statement that is derived logically from the factual
statement is the equivalent logical statement. To implement logical equivalence, one needs to
divide the statements into two parts: the hypothesis and the conclusion (Heyninck and Arieli
2019). The hypothesis is the fact that is revealed in the sentence. The conclusion is the second
part of the sentence that is derived based on the first statement.
The contrapositive statement is constructed from a sentence after implementing the
converse and the inverse logics on the statement. Firstly, the sentence has to be divided into
two parts called the hypothesis and the conclusion. Once this division is done, the hypothesis
and the conclusion needs to be switched with each other. After the positions are exchanged,
negation is applied to both the parts of the statement by which the contrapositive statement is
formed.
For example, in a sentence, ‘If two angles are congruent, they have the same
measure’. The hypothesis part of the statement is ‘if two angles are congruent’ and the
conclusion is the ‘they have the same measure’. Switching the statements, the sentence
becomes ‘The two angles have same measure, if they are congruent’. After applying

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negation, the sentence is ‘If the two angles don’t have the same measure they are not
congruent’. This contrapositive statement is formed from the given statement.
The contradiction of a logic is a statement that contains both the truth and the false
and that contradicts with each other (Chamberlain Jr and Vidakovic 2017). The statement
comprises of a sentence in the first part and exactly the negation of it in the second part.
Thus, the result obtained after the ‘AND’ operation applied on the statement is always false.
For example, in the sentence, ‘I am going to college and I am not going to college’, the
second part of the sentence is the negation of the first part. This contradiction is displayed
within a statement.
Answer 3:
Brute-force is a password hacking methodology adopted by the hackers for hacking
accounts from different web pages or websites. By this trial and error method of brute-force
attack, the hackers make all the permutations and combinations possible from an assumed
password hoping that one of them will be the actual password available amongst the lot
(Arzhakov and Silnov 2016). To implement brute-force attack on passwords, the hackers
have invented various tools that will help their job easier. Some of these tools are the Brutus,
Medusa, Ncrack and many more that helps in extracting passwords within no second.
Including the uppercase and lowercase characters of the English alphabets along with
the ten numbers from 0 to 9, there are in total {(26*2) +10} = 62 characters. Now in case of
the password ‘guitarcheesefruit’, the number of characters available here is 17. Hence, the
possible combinations that can be made to crack this password is 6217. However, in case of the
password ‘hunter12’, the possible combinations that can be made is 628. The former one is
simple but longer, while the latter one is complex but shorter. Hence, the first password
‘guitarcheesefruit’ is the harder one to crack with a huge number of combinations.

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The web administrators can implement various techniques to avoid brute-force attack
method for hacking passwords and getting unauthorized access to accounts (Pawar and Dani
2017). They should implement a technical procedure called the ‘salt and hash’ on the
passwords, such that the hackers can only hack the network but not get access to the accounts
by hacking the passwords. The administrators should suggest on making the passwords
lengthy enough including a combination of both upper and lower case characters as well as
the numerical numbers to make a strong password.
Answer 4:
Automation is the application of technologies in the modern industries as well as the
renovation of the ancient methods in the old industries in order to replace the manual labour
and increase the pace of task completion (Noble 2017). In clear and simple words, invention
of machineries that will understand the manual work pattern and act accordingly such that the
same work is done more accurately in a shorter span of time is known as the application of
automation. Human labour is discarded and new machines are added to the organizations for
the automation revolution nowadays. The areas of application of automation are
manufacturing of items, transporting them, operational works and most importantly in IT
sectors. A broad range of technologies such as implementation of robots and drones, cyber
security measures, sensors, wireless applications, telecommunications are the major
inventions of automation in the industries.
In the sector of automation, state machine is an automation type by which different
conditions or states are implemented such that the operations are carried out one after another
(Parasuraman 2017). There can be many conditions when the machines have to take decisions
between the different options. These options are treated as states or conditions that the
machines work on. If an activity occurs, the respective state assigned is triggered. When the

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activity ends, the state exits or changes into another state by the change of activity. The
arrows represent these changes of states. There exists three parts in a state, the ‘Entry’, the
‘Exit’ and the ‘Transition’. The ‘Transition’ is the phase where the change of state occurs
when one activity expires and another activity starts.
Answer 5:
The Cartesian product of sets is a multiplication that is applied on the sets in an
ordered way such that each element of one set intersects with each element of the other set.
Coming to the Cartesian product, there shall exist two sets (Selvam and Nagalakshmi 2016).
The primary condition for these sets for form a Cartesian product is that, it should be non-
null.
For the given sets A and B, where A = {rock, paper, scissors} and B = {metal, plastic,
wood}, the Cartesian product of
A X B = {(rock, metal), (rock, plastic), (rock, wood), (paper, metal), (paper, plastic), (paper,
wood), (scissors, metal), (scissors, plastic), (scissors, wood)}; and
B X A = {(metal, rock), (metal, paper), (metal, scissors), (plastic, rock), (plastic, paper),
(plastic, scissors), (wood, rock), (wood, paper), (wood, scissors)}
The language of aΣ^* Σ^* a is an expression in a simple computation language used∪
in automata known as the ‘Regular Language’ in the branch of automata where the states are
expressed using regular expressions. This language consists of some set of strings, symbols,
or characters that are used in the computability theory by which programming languages
were designed. Since the regular languages are composed by using all types of strings, hence
they can be considered as the subset of the strings (Harden 2017). In automata, this language
is used to compute the diagrams of state machines for its formation.

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References
Arzhakov, A.V. and Silnov, D.S., 2016. Analysis of Brute Force Attacks with Ylmf-pc
Signature. International Journal of Electrical & Computer Engineering (2088-8708), 6(4).
Button, T., 2016. Knot and Tonk: Nasty connectives on many-valued truth-tables for classical
sentential logic. Analysis, 76(1), pp.7-19.
Chamberlain Jr, D. and Vidakovic, D., 2017, February. Developing student understanding:
The case of proof by contradiction. In Proceedings of the 20th Annual Conference on
Research in Undergraduate Mathematics Education.
Geuvers, H. and Hurkens, T., 2017, January. Deriving natural deduction rules from truth
tables. In Indian Conference on Logic and Its Applications (pp. 123-138). Springer, Berlin,
Heidelberg.
Harden, C., 2017. Regular Expressions For IT Men.
Heyninck, J. and Arieli, O., 2019, June. Simple contrapositive assumption-based frameworks.
In International Conference on Logic Programming and Nonmonotonic Reasoning (pp. 75-
88). Springer, Cham.
Noble, D., 2017. Forces of production: A social history of industrial automation. Routledge.
Parasuraman, R., 2017. 1 Application of human performance data and quantitative models to
the design of automation. Engineering Psychology and Cognitive Ergonomics: Volume 5:
Aerospace and Transportation Systems, p.3.
Pawar, A.V. and Dani, A.R., 2017. Privacy preserving framework for brute force attacks in
cloud environment. International Journal of High Performance Computing and
Networking, 10(1-2), pp.91-99.

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Selvam, P.S. and Nagalakshmi, K.T., 2016. Role of homomorphism and Cartesian product
over fuzzy PMS-algebras. International Journal of Fuzzy Mathematical Archive, Accepted
for Publication.