Logic
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Logic

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Logic Logic Presentation Transcript

  • Logic
  • Propositions• An assertion which is definitely either true or false is called a proposition, shown by the letters p, q, r, s, ….• Examples:• Dogs with six legs.• 2+3=5• Come here.• Who is that?• The triangle is negative.
  • Truth values of proposition• The truth and falsity of a proposition is called its truth value. The numbers 1 and 0 are used as the truth values of the true and false propositions respectively. p true 1 p false 0
  • p q 1 1 1 1 q 0 1 0p 1 0 1 0 q 0 0 0
  • Equivalent propositions• Two propositions p and q have the same truth value they are said to be equivalent propositions, denoted as
  • Negation of a proposition• The negation of a proposition p is denoted by p’ . The following table provides some information about negation. p p’ Some symbols negation 1 0 = ≠ 0 1 > ≤ ≥ <
  • Compound Propositions• A proposition which is formed two or more propositions by using connective words is called a compound proposition. Connective Words: And Or Then If and only if
  • Connective Symbol Name and ∧ conjunction or ∨ DisjunctionIf …. then …. => Implication (implies)If and only if  Equivalence
  • Conjunction ∧• A compound proposition of p and q formed using the connective word “and” is called conjunction of p and q, written as p∧q.• The conjunction of p and q is true if both p and q are true otherwise it is false. p q p∧q 1 1 1 1 0 0 0 1 0 0 0 0
  • Disjunction ∨• A compound proposition of p and q formed using the connective word “or” is called disjunction of p and q, written as p∨q.• The disjunction of p and q is false if both p and q are false otherwise it is true. p q p∨q 1 1 1 1 0 1 0 1 1 0 0 0
  • Common properties of ∧ and ∨
  • Common properties of ∧ and ∨
  • Common properties of ∧ and ∨