Understanding Simple Logic Statements

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’

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.

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’