Simple Logic

Statement(命題) A sentence which has the property of being true (T) or false (F) is called Statement or Proposition. (Usually denoted by p, q, r, … etc.)

Conjunction(合取 )： ‘p and q’ denoted by ‘p ^ q’. disjunction (析取 )： ‘p or q’ denoted by ‘p v q’. negation (否定)： ‘ ~ p’

p q p ^ q p v q ~ p T F

Logically Equivalent (邏輯等價 ) or Equivalent (簡稱為等價 ) Symbol: ‘≡’

Conditional Proposition (條件命題 ) ‘if p then q’ denoted by ‘p → q’

sufficient condition (充分條件 ) necessary condition(必要條件) There are several ways in which “if p then q” can be expressed: (i) p  q. (ii) p is a sufficient condition for q. (iii) q is a necessary condition for p. (iv) p only if q.

p q p → q T F

Derivatives (條件命題的衍生命題 ) If ‘p → q’, then the converse (逆命題 ) q → p ; the inverse (否命題) (~p) → (~q)； the contrapositive (逆反命題 )(~q) → (~p). Note: ‘p → q’ ≡ ‘(~q) → (~p)’; ‘q → p’ ≡ ‘(~p) → (~q)’

Biconditional Proposition(雙條件命題 ) p↔q

Other Symbols ‘’ means ‘for all’ ‘’ means ‘there exists’