1. Simple Logic

2. 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.)

3. 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’

4. p q
p ^ q
p v q
~ p T F

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

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

7. 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.

8. p q
p → q T F

9. 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)’

10. Biconditional Proposition(雙條件命題 )
p↔q

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