Discrete Math

Discrete Math

1. branch of mathematics that deals with the study of finite objects that is an object that can be counted.

2. Propositions and Truth Tables

   • Proposition - is any simple (also called automic) declarative statement is either true or false, yes or no, 1 or 0 but not both.
   • Sentence - express a complete thought / idea
     • Kinds of sentence
       • Declarative- gives information, narrative, statement
       • Imperative- command/ request
       • Exclamatory- express feelings/ emotions
       • Interrogative- asks question.

3. Logic - is an art or science of correct or valid reasoning.

4. Logical Connectives & Truth Tables

   • ~ : not / meaning opposite or reverse.
   • v - OR : if one statement is true then the answer is true.
   • ^ - And : if one statement is false then the answer is false.
   • --> - IF .. THEN - T--> F = F , F-->T= T , F-->F = T , T-->T=T
   • <---> - Biconditional T<--> T , F<-->F , T <-->F, F <--> T (FALSE)

5. Tautologies, COntradiction & Contingencies

   • Tautology- true for all possible truth values of its constituent propositional variables
   • Contradiction: compound proposition that is false for all possible truth values of its constituent propositional variables.
   • Contingency - a compound proposition that is neither a tautology nor a contradiction - whose truth tables exhibit some T and some F entries.