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Transcript of Logic (PROPOSITIONS)

  • By D .Nayanathara (BSc in MIS)By D .Nayanathara (BSc in MIS)
  • SENTENCE THAT IS ETHIER TRUE (T)OR FALSE(F) Ex 3 + 5 = 8 : Proposition 9 - 2 = 5 : Proposition a < b : Not a Proposition Who can speak French: Not a Proposition
  • PRIMITIVE PROPOSITION - Can not be broken down in to simple proposition. COMPOSITE OR COMPOUND PROPOSITION Can be broken down in to two or more primitive propositions. Ex 2+3 = 5 and 1+7 = 4 Birds can fly or Today is hot.
  • Name Symbol Operation Negative not ~ Disjunction or Conjunction and
  • Proposition variables used to describe proposition Propositional Variable is variable which either true or false In logic p,q,r ,.. Letters used to indicate these variables Ex: p indicate negative of the p
  • Truth table lists whether a statement is true or false. Truth Tables defined the logical connectives of the compound statements(compound propositions). The sentences built out of propositions and logical connectives are also propositions. They have truth values.
  • Column must be allocated for each proposition variables in the compound statement and for the final compound proposition. Truth Tables should contain all the possible combinations (truth values) of T and F values for all proposition variables.
  • Number of rows in truth table indicates by 2n where n is the number of propositions. Ex : Birds can fly or Today is hot. 1. Birds can fly 2. Today is hot There are two propositions in the compound statement : n = 2 So, Number of rows (combinations) = 22 = 4
  • p p T F F T
  • p q p v q T T T T F T F T T F F F
  • p q p q T T T T F F F T F F F F
  • p pv p T T F T Ex :pv( p q) Formula which is always True (or T )
  • p q p q ~(p q) pv~(p q) T T T F T T F F T T F T F T T F F F T T Ex : pv( p q)
  • p p p T F F F Ex: (pv (not p)) ((p (not p)) (p q) not(pvq) Formula which is always False (or F)
  • p q p q p v q ~(p v q) (p q) ~(p v q) T T T T F F T F F T F F F T F T F F F F F F T F Ex : (pq) ~(pvq)
  • p q p q T T T T F F F T T F F T If p then q
  • p q p q T T T T F F F T F F F T p if and only if q (iff)