FORMAL LOGIC

Symbolic Logic

Symbolic logic is the method of representing logical expressions through the use of symbols and variables, rather than in ordinary language. This has the benefit of removing the ambiguity that normally accompanies ordinary languages, such as English, and allows easier operation.There are many systems of symbolic logic, such as classical propositional logic, first-order logic and modal logic. Each may have seperate symbols, or exclude the use of certain symbols.

Logical Symbols

The following table presents several logical symbols, their name and meaning, and any relevant notes. The name of the symbol (under meaning links to a page explaining the symbol or term and its use). Note that different symbols have been used by different logicians and systems of logic. For the sake of clarity, this site consistently uses the symbols in the left column, while the Notes column may indicate other commonly-used symbols.

LOGIC SYMBOLS

What is logic?Simply the study of correct reasoningProposition building block of logic simple declarative sentence that can be either true or false but not both

Truth Table for Propositional Connectives

EXAMPLESP- The spaghetti is hotQ- The pizza is coldR- The chicken will be deliveredP ^ ~RThe spaghetti is hot and the chicken will not be deliveredQRIf the pizza is cold then the chicken will be deliveredQ V ~REither the pizza is cold the chicken wont be delivered

EXAMPLESP A human is a cat Q Squares have corners

P -> Q If a human is a cat then squares have corners

Statement in symbolsTruth Value of partsTruth value of entire statement P -> Q F -> T TRUE

PQP->QTTTTFFFTTFFT

EXAMPLESA- Basketball is a team sport.B- Sport games are fun.C- The people are boring.A^B = Basketball is a team sport and sports games are fun.B C = Its either sport games are fun or the people are boring.B^C= Sport games are fun and the people are boring.A^C = Basketball is a team sport and the the people are not boring.(A B) C= Its either basketball is a team sport or sport games are fun, or the people are boring.

EXAMPLES 1.)p : Every organism has a heartq : All organisms have emotions

p and q :All organisms have emotions and every organism has a heart.

2.)

The art show was enjoyable and the room was hot.

P: The art show was enjoyable.Q: The room was hot.

EXAMPLESStatement: If Memorial Day is a holiday then we do not work on Memorial Day.

Let a represent "We go to school on Memorial Day." Let b represent "Memorial Day is a holiday." Let c represent "We work on Memorial Day."

EXAMPLES(Cireel?)If a mapuan will take physics and math at the same time , then he cant pass it both. Trinidad is taking physics and math at the same time. Therefore he cant pass it both.

Let : A = If a mapuan will take physics and math at the same timeB = he cant pass it both.

EXAMPLES(Mark Tiongco) If I'm going to do well on this quiz, then I will have a better test score. If I will have a better test score, then my grade in logic will be good. I'm not going to do well on this quiz. Therefore, my grade in logic will not be good.

LetA - I'm going to do well on this quiz B - I will have a better test score. C- My grade in logic will be good.

EXAMPLES(John Rey Trinidad)If Torano is the ALAY in HUM17, then I will pass the course.Torano is the ALAY. Therefore I will pass the course.

Let:A = Torano is the ALAY in HUM17B = I will pass the course

EXAMPLES(Samuel Timogan)If Ninoy is the President of the Philippines, then he must have been elected by the Filipino people. Ninoy was voted by the people. Therefore Ninoy is the President of the Philippines

Let:A- Ninoy is the President of the PhilippinesB- he must have been elected by the Filipino people

EXAMPLES(Kimberly Sison)If the tire is flat then I will have to remove it and take it to the gas station.

P: The tire is flat.Q: I have to remove the tire.R: I have to take the tire to the gas station.

ANSWERS (SESE)Condition: q^p

A . B = Basketball is a team sport and sports games are fun

ANSWERS (MARK TIONGCO)~A

ANSWERS (Cireel)

ANSWERS (John Rey Trinidad)

ANSWERS (TIMOGAN)

ANSWERS (KIMBERLY SISON)Conditional: P -> (Q ^ R)

ANSWERS (RABINO)Conditional: B ~C

BC~CB^~CTTFFTFTTFTFFFFTF