Bi Implication Inwards Mathematical Logic

Definition of Bi Implication

Two statements p together with q tin last made into a novel contestation or chemical compound judgement into the cast "p if together with solely if q". This novel contestation prepared inwards such a means is called the contestation of the bi iden- tation of the statements p together with q.

Formula Bi Implications inwards Mathematical Logic

p ↔ q

Information :
p ↔ q reads "p if together with solely if q"

Example Bi Implications inwards Mathematical Logic

p : v > 1
q : 3² = 9
p ↔ q: v > ane if together with solely if 3² = 9

Truth value tabular array of Bi Implication

The truth value of the biimplication contestation is determined every bit follows:

The p ↔ q bi implication is truthful if p together with q accept the same truth value. In other possibilities bi implications are false.

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Implications Inwards Mathematical Logic

Two statements p too q tin last made into i novel tilt of chemical compound sentences into the shape "if p hence q". New statements arranged inwards this agency are either implied statements or conditional / conditional statements of p too q statements. The "if p" role is called the argue or campaign (antecedent / hypothesis) too the "then q" is called conclution or resultant (conclusion or consequence).

Formula of Implications

p → q 

Information:
p → q reads "if p hence q"

Examples of Implications inwards Mathematical Logic

p    : It's a cloudy day
q    : Now it volition rain
p → q: If it's cloudy at in i trial it volition rain

Truth Table of Implications

The value of the truth of the implication tilt is determined past times the truth value of each percentage non past times the human relationship of the 2 sole statements. The value of truth implication is every bit follows:

The implication p → q is imitation if p is truthful too q is wrong, inwards other probability p → q is true.

Information :
T : True
F : False/wrong

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Disjunction Inward Mathematical Logic

Two statements p in addition to q tin endure combined using a hyphen "or" to shape a novel statement. This chemical compound arguing is called a disjunction. The disjunction of the p in addition to q statements is written "p ν q" in addition to read "p disjungs q" or "p or q".

In everyday life the discussion "or" agency ane or both, it tin endure either merely non both.

Formula of Disjunction

p ν q

Information :
p ν q read "p or q"

Example of Disjunction inwards Math Logic

p    : Two lines are parallel
q    : Two lines intersect
p ν q: Two lines are parallel or intersect each other

Truths value of Disjunction Table

The value of the truth of the multiple disjunction statements of 2 statements p in addition to q is determined every bit follows:

If p is truthful in addition to q is valuable or p in addition to q are both truthful in addition to thence p ν q is true. If non in addition to thence p ν q is wrong. In other words the disjunction of 2 statements is imitation alone if the 2 components are wrong.

Information :
T : True
F : False/Wrong

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Conjunction Inwards Mathematical Logic

Definition of Conjunctions inwards Mathematical Logic

Two statements p as well as q tin travel combined using the "and" hyphens to cast a chemical compound tilt called the conjunction of the p as well as q statements. The conjunction of the p as well as q statements is expressed by:

Formula or symbol of Conjunctions inwards Mathematical Logic 

p ∧ q

Information :
p ∧ q read "p as well as q"

Example of Conjunctions inwards Mathematical Logic

p : Djakarta is the Capital of Indonesia
q : Djakarta is located on the isle of Java
p ∧ q : jakarta is the uppercase of Republic of Indonesia as well as is located on the isle of Java.

Truth value of Conjunction

The truth value of the conjunctive chemical compound tilt of 2 statements p as well as q is determined equally follows :

If p is truthful as well as q is truthful hence p ∧ q is true. If 1 of the statements is faux hence p ∧ q is false.

Information :
T = True
F = False or wrong

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Statements As Well As Non Statements Inwards Math Logic

In everyday life, if you lot desire to limited something, together with thus ever purpose the judgement (a serial of words). According to the logic of the judgement system is every bit follows:

1. Meaning Sentence

Sentence agency meaningful sentence

Example of Meaning Sentence

Fatima is a 10th grader
Jakarta is located on the isle of Java
6 x 8 = 50

2. Not Meaning Sentence

Not Meaning Sentence is a judgement that has no meaning

Example of Not Meaning Sentence

The depository fiscal establishment loves eight
Three dining cabinets

3. Statement Sentence

The contestation judgement is a judgement that has truthful or imitation values only, but non both. Thus nosotros tin say that the contestation is a judgement that has truthful value entirely or incorrect asja but non truthful together with incorrect all at once, or inward other words a contestation is a judgement that tin live on determined the value of truth. To simplify subsequent use, the contestation volition live on denoted past times a small-scale letter, such every bit p, q, r together with thus on. The truthful contestation has a truthful value of T (true) or 1 together with the imitation contestation has a T (wrong) or 0 truth value.

Example of Statement Sentence

p: The counting set out is the master summation the zero
q: Republic of Indonesia Raya vocal created past times Kusbini
r: If 2x = vi together with thus x = 3

In the event of the contestation above, p together with r are truthful piece q is false.

4. Statement of facts Sentence

Statement of facts Sentence is a contestation whose truthful value should live on investigated first.

Example of Statement of facts Sentence

Hanif is ane of the students of SMK Taruna
Fulan is a corrupt person
There has been a burn at Bumi Maya Housing

5. Not Statement Sentence

Not Statement Sentence is a judgement that tin non live on determined its truthful value.

Example of Not Statement Sentence

May God forgive your sins
What is the set out of students of SMK inward Jakarta?
Rest if you lot are tired

6. Open sentence

Open judgement is a judgement containing variable (variable) together with if the variable is replaced past times a constant inward its semestation, it volition attain a statement.

Exmaple of Open sentence

x + 2 = 5
x² - 5x - twoscore > 0
This is a metal

Influenza A virus subtype H5N1 variable inward the opened upward sentence, if it is replaced together with thus the judgement tin live on determined its truthful value. Review x + 2 = 5, if x nosotros supervene upon amongst 3 together with thus the judgement becomes 3 + 2 = 5 is a judgement that is truthful together with x = 3 is called completion of the opened upward sentence. But if the cost of x nosotros supervene upon amongst 1 together with thus the judgement becomes 1 + 2 = 5, this is a contestation that is incorrect value.

From the higher upward review nosotros tin say that the opened upward judgement tin plough into a contestation that is truthful or imitation if the variable or variable of the opened upward judgement is replaced amongst a certainly value.

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Compound Statements Inwards Math Logic

Definition of Compound Statements inward Mathematical Logic

Influenza A virus subtype H5N1 chemical compound tilt or multiple judgement is a novel tilt composed of 2 or to a greater extent than statements using the discussion logic, ie and, or only in addition to then on. The tilt of the chemical compound of the chemical compound tilt is called the components or sub-statements.

Example of Compound Statements inward Mathematical Logic

Bandung the uppercase of West Java province in addition to located on the isle of Java.
Component forming chemical compound judgement is Bandung the uppercase of West Java in addition to Bandung is located inward West Java.

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Negation Inwards Mathematical Logic

Definition of Negation inwards Mathematical Logic

Negation is normally used to deny or opposite a statement. To deny or brand a negation of a disceptation is normally yesteryear putting the give-and-take "not true" inwards forepart of a judgement or yesteryear inserting not. "The novel disceptation obtained inwards such a means is called the negation of an initial statement.

Formula or Symbol of Negation inwards Mathematical Logic

If p is a statement, the negation of the disceptation tin flame last written equally follows:

p

Information :
p reads "not truthful p" or "not p"

Example Question of Negation inwards Mathematical Logic

Please possess upwards one's heed the negation of the statements:
p: DKI Jakarta upper-case missive of the alphabet of Indonesia
p: Not truthful DKI Jakarta upper-case missive of the alphabet of Indonesia
p: DKI Jakarta is non the upper-case missive of the alphabet of Indonesia

Truth Value of Negation

If p is a truthful value, in addition to therefore p is incorrect in addition to vice versa if it is imitation in addition to therefore p is true, for the truth tabular array it tin flame last seen inwards the truth tabular array below:

Information :
T = True
F = False / Wrong.

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