tags: CISC1002 chapter1-1

Propositions - Logical Operations

• Negation (“非”) : ¬p
• Conjunction (“并且”又称”合取”) : p /\ q
• Disjunction (“或者”又称”析”取) : p \/ q
• Exclusive (“异或”) : p
  $⨁$ q
  
  
• Implication (“蕴含”) : p → q
• Biconditional (“当且仅当”又称”等价”) : p↔q

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Truth table

• Negation Truth table

  p	¬q
  T	F
  F	T

• Conjunction Truth table

  p	q	p /\ q
  T	T	T
  T	F	F
  F	T	F
  F	F	F

• Disjunction Truth table

  p	q	p\/q
  T	T	T
  T	F	T
  F	T	T
  F	F	F

• Exclusive Truth table

  p	q	p $⨁$ q
  T	T	F
  T	F	T
  F	T	T
  F	F	F

• Implication Truth table

  p	q	p→q
  T	T	T
  T	F	F
  F	T	T
  F	F	T

• Biconditional Truth table

  p	q	p↔q
  T	T	T
  T	F	F
  F	T	F
  F	F	F

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Precedence(優先順序) of Logical Operations

Operatop	Precendence
¬	1
/|2
\/	3
→	4
↔	5

• ¬
  $>$ /\
  $>$\/
  $>$ →
  $>$ ↔