Logic
Propositions• An assertion which is definitely either true or  false is called a proposition, shown by the letters  p, q, ...
Truth values of proposition• The truth and falsity of a proposition is called  its truth value. The numbers 1 and 0 are us...
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,...
Negation of a proposition• The negation of a proposition p is denoted by  p’ . The following table provides some  informat...
Compound Propositions• A proposition which is formed two or more  propositions by using connective words is called a  comp...
Connective       Symbol     Name    and            ∧      conjunction     or            ∨      DisjunctionIf …. then ….   ...
Conjunction ∧• A compound proposition of p and q formed  using the connective word “and” is called  conjunction of p and q...
Disjunction ∨• A compound proposition of p and q formed  using the connective word “or” is called  disjunction of p and q,...
Common properties of ∧ and ∨
Common properties of ∧ and ∨
Common properties of ∧ and ∨
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Logic

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Logic

  1. 1. Logic
  2. 2. 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.
  3. 3. 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
  4. 4. p q 1 1 1 1 q 0 1 0p 1 0 1 0 q 0 0 0
  5. 5. Equivalent propositions• Two propositions p and q have the same truth value they are said to be equivalent propositions, denoted as
  6. 6. 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 > ≤ ≥ <
  7. 7. 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
  8. 8. Connective Symbol Name and ∧ conjunction or ∨ DisjunctionIf …. then …. => Implication (implies)If and only if  Equivalence
  9. 9. 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
  10. 10. 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
  11. 11. Common properties of ∧ and ∨
  12. 12. Common properties of ∧ and ∨
  13. 13. Common properties of ∧ and ∨

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