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Symbolic logic

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  • 1. SYMBOLIC LOGIC Statement Connectives How to prove? Quantor validity
  • 2. SYMBOLIC LOGIC Statement Statement Variable & Constanta Open Sentence Connectives How to prove? Quantor validity
  • 3. SYMBOLIC LOGIC Statement Statement Variable & Constanta Open Sentence Connectives How to prove? Quantor validity A statement is a declarative sentence, which is to say a sentence that is capable of being true or false. The following are examples of statements. it is raining I am hungry 2+2 = 4 God exists On the other hand the following are examples of sentences that are not statements. are you hungry? shut the door, please #$%@!!! (replace ‘#$%@!!!’ by your favorite expletive)
  • 4. SYMBOLIC LOGIC Statement Statement Variable & Constanta Open Sentence Connectives How to prove? Quantor validity Variable is a symbols which is point to unspecified members of the universal Constant is a symbol which is point to specific element in the universal Example: An straight line equation y = 2x + 3 Which one are variables or constant?
  • 5. SYMBOLIC LOGIC Statement Connectives How to prove? Quantor validity Statement Variable & Constanta Open Sentence Open sentence is a sentence with variables and if the variables was substituted with the constat in the universal then you can determine it is true statement or wrong statement
  • 6. SYMBOLIC LOGIC Statement Negation Disjungtion Conjunction Implication Biimplicatio n Connectives How to prove? Quantor validity
  • 7. SYMBOLIC LOGIC Statement Negation Disjungtion Connectives How to prove? Quantor validity A (statement) connective is an expression with one or more blanks (places) such that, whenever the blanks are filled by statements the resulting expression is also a statement. Conjunction Simple statement is a a statement that is not constructed out of smaller statements by the application Implication of a statement connective Biimplicatio n constructed from one or more simplestatements by Compound statement is a statement that is the application of a statement connective.
  • 8. SYMBOLIC LOGIC Statement Negation Connectives How to prove? Quantor validity Negation of a statement is a new statement which is true if the truth of the first statement is false and Disjungtion conversely. Symbolized by : - or ¬ or ~ Conjunction Means: “ not”, “no”, “it is not true (false) that”, “it cannot Implication Example: Biimplicatio n be that”, it is imposible that”, etc 1. p :This two things are similar 2. ~p: this two things are not simmilar
  • 9. SYMBOLIC LOGIC Statement Negation Connectives How to prove? Quantor This is summarized in the following truth tables. Disjungtion p Conjunction Implication Biimplicatio n ~p B S S B Note: ~d has the opposite truth value of d. validity
  • 10. SYMBOLIC LOGIC Statement Negation Disjungtion Conjunction Implication Biimplicatio n Connectives How to prove? Quantor validity Disjunction is corresponds roughly to the English ‘or’. The symbol for disjunction is “ ˅ “ (wedge). In English, the word ‘or’ has at least two different meanings, or senses, which are respectively called the exclusive sense and the inclusive sense So there are two types of disjunction: 1. Inclusive Disjunction A disjunction p ˅ q false if both disjuncts are false; is otherwise, it is true 2. Exclusive Disjunction A disjunction p ˅ q false if both disjuncts are the same is truth; otherwise, it is true
  • 11. SYMBOLIC LOGIC Statement Connectives How to prove? Quantor validity Negation Conjunction is corresponds to the English expression Disjungtion „and‟. The symbol for conjunction is “ ˄ “ Conjunction Deffinition: A conjunction p ˄ q is true if both conjuncts are true; Implication Biimplicatio n otherwise, it is false
  • 12. SYMBOLIC LOGIC Statement Negation Connectives How to prove? Quantor validity the conditional connective is corresponds to the expression Disjungtion if ___________, then ___________. The symbol used to abbreviate if-then is the arrow (→) Conjunction „if‟ introduces the antecedent „then‟ introduces the consequent Implication Biimplicatio n A conditional d → f is false if the antecedent d is true and the consequent f is false; otherwise, it is true.
  • 13. SYMBOLIC LOGIC Statement Connectives How to prove? Quantor validity Negation the biconditional is corresponds to the Disjungtion English ______________if and only if _______________ Conjunction The symbol for the biconditional connective is „ ↔ ‟ A biconditional d ↔ e is true if its constituents have the Implication Biimplicatio n same truth value; otherwise,it is false
  • 14. Statement Negation Disjungtion Conjunction Implication Biimplicatio n Connectives How to prove? Quantor
  • 15. Statement Negation Disjungtion Conjunction Implication Biimplicatio n Connectives How to prove? Quantor