LOGIC MATH101

LOGIC

Logic is concerned with the correctness of

reasoning and thinking. When a lawyer appears in a court,

he applies logic in the presentation of his client's case to

the judge. The judge also applies logic to give his verdict

From day to day, every human being applies the art of

reasoning in taking decisions affecting his or her 1life.

Decrees, laws and pronouncements formulated by the

government were as a result of certain reasoning.

Professional football involves

lot

of

reasoning/thinking that in a competition. a player who

bags two yellow cards in a match is equivalent to have

bagged a red card in a match. Such player suffers the

punishment of leaving the pitch and must not play in the

next match within the same season. Therefore. logic is

also the ability to draw

suitable inferences and

conclusions after a persuasive argument. The logician is

the relationship

premises/hypotheses and the conclusion of an argument.

His question is whether the conclusion follows validly

interested in

between

the

from the premises.

Logic 1s not concerned with the truth or falsity of

An individual propositions that represents the premises

and the conclusion.

Example I: All DPO are Policemen

u

Valid

Valid

All Police men are men

All DP0 arc men

11 victory is a female student in SS II

All SS Il Female students are members of the volley ball

team.

Victor is a member of the volley ball team.

NOTE: If the conclusion follows correctly from the

premises, the argument is valid. Thus, we speak of valid

arguments and not true arguments, and of true

propositions and not valid proposition's.

To a mathematician, an argument on what is as

opposed to "what is not" & an not be held as foolproof until

they satisfy set rules which we will soon discuss.

In summary, logic is the science of deductive

In

reasoning by using symbols and sticking strictly to set

down rules.

The Three Laws of Thought

The following laws are necessary in order for

reasoning to proceed correctly:

A. Law of Identity: This states that if a proposition is

true, then it is true. Logically, P P. Every

proposition implies itself.

both true and false.

proposition can be either true or false.

B. Law of Non Contradiction: No proposition can be

C. Law of Excluded Middle: This states that a

Proposition/Statement

Proposition 1s a statement which may be judged

true (T) or false (F), but not both. Let us look at few

examples of propositions.

i)Today is Wednesday

ii) Martin is a boy

ii)8 is greater than 6

iv) All mathematicians re magicians

v) Edem is in Enugu State. etc.

NOTE: Not all statements are propositions.

Examples:

i) What is coming?

11) What class are you?

i) Your statement is true?

iv) Give me a chalk etc.

Proposition therefore, consists of statements and sub

statements which are either true or false. The examples of

above proposition are simple statements.

Compound Proposition/Composite Proposition

A Compound or composite proposition is one

obtained by combining two or more propositions with

Connectives (such as and or'). in other words

Compound proposition can be described as when two or

more simple statements are linked together to form one

Sentence. Examples of compound statement are:

1. She is tall and dark in complexion.

2. "x is equal to 4 or x is equal to 5.

3. Ada is hungry and she eats.

4. parallelograms on the same base and between the same

parallels are equal in area.

5. Okocha is an athletic or a footballer, etc.

TRUTH VALUES

The truth or falsity of a statement is called its truth

values. Example: Determine,, which of the following

propositions are true or false

i)

ii) Mary is not a girl (false)

iii) USA is in Africa State (false), etc.

NOTE: True (T) and False (F) = Truths values.

5+3 8 (True)

TRUTH TABLES AND BASIC LOGICAL

"CONNECTIVES

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