Logical Operator

• Negation - It is also represented by “not”.
• What is in the picture?

  A) Negation

  
• Conjunction (^) - This is a binary operator, meaning it uses two propositions where "p ∧ q" is true if both propositions are true.
• Conjunction (^) - It is also represented by “and”.
• What is in the picture?

  A) Conjunction

  
• Disjunction (V) This is a binary operator, meaning it uses two propositions where "p v q" is true if at least one or both propositions are true.
• Disjunction (V) - It is also represented by “or”.
• What is in the picture?

  A) Disjunction

  
• Implication (->) This is a binary operator, meaning it uses two propositions where "p -> q" is false if p is true and q is false.
• Implication (->) - It is also represented by “if… then…”.
• What is in the picture?

  A) Implication

  
• Implication (->)

  • p is called the premise, hypothesis, or antecedent.
  • q is called the conclusion or subsequent.
• Other structure of implication:

  • Converse (q → p)
  • Inverse (¬p → ¬q)
  • Contrapositive (¬q → ¬p)
• Biconditional ( <-> or ≡) This is a binary operator, meaning it uses two propositions where "p <-> q" is true if p and q propositions have the same truth value.
• Biconditional - It is also represented by “if and only if”.
• What is in the picture?

  A) Biconditional

  
• Exclusive OR (△ or ⊕) - This is a binary operator, meaning it uses two propositions where "p △ q" is true if both p and q propositions have different truth values.
• What is in the picture?

  A) Exclusive OR

  
• Precedence of logical operators can help to determine which operation needs to be evaluated first in a given compound proposition like p v q ^ 7p v (p -> q).
• Precedence of logical operators

  • Negation
  • Conjunction
  • Disjunction
  • Implication
  • Biconditional
• Negation (~) - This is a unary operator, meaning it uses only a single proposition where it reverse the truth value of a proposition.