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皮从
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1 Chapter

2 2 1.1 truth Tfalse F (proposition) (1) (T) (2) 2+3=6(F) (3) 1+2=3 (atom proposition)(primary proposition) (compound proposition)(1)(negation)(2) (and)(3)(or) 1+1=2 1+1=2 52=6

3 Chapter 01 3 (T)(F) p, q, r, p, q, r, (propositional variables) (truth table) r 2 r 2 r 2 r () p p~p p (T)~p (F) p (F)~p (T)~p p ~p T F F T

4 4 (T) (F) () p, q p q p q p, q (T) p q (T)(F) p q p q T T T F T F T F F F F F p q p q (conjunction) (conjunction operator) (1) 5+2=6 (2) 5+2=6 (3) 5+2=7 (1) 5+2=6 5+2=6

5 Chapter 01 5 (2) 5+2=6 5+2=6 (3) 5+2=7 5+2=7 () p, q p q p q p, q (F)p q (F)(T) p q p q T T T F T T T F T F F F p q p q (disjoint) (disjoint operator) (exclusive or) p q p q (T) p q p q p q T T F F T T T F T F F F

6 6 ~[p (~q)] q p q ~ [p ( ~ q)] q T T T F F T F T T F F T T F F T T F F F T F T T ( p q) (~ p) p q (p q) ( ~ p) T T T F F F T T T T T F T F F F F F F T

7 Chapter 01 7 P 1 (p 1, p 2 p n )P 2 (p 1, p 2 p n ) P 1, P 2 P 1 P 2 P 1 P 2 P 1 P 2 P 1 P 2 ~(p ~q)~p q T (tautology)f (contradiction)

8 8 p qq p p qq p p (q r)(p q) r p (q r)(p q) r p pp p pp p (p q)p p (p q)p p (q r) (p q) (p r) p (q r) (p q) (p r) ~(p q)~ p ~q ~(p q)~ p ~q ~(~p)p p Tp p Fp p FF p TT p ~pf p ~pt ~(p ~q)~ p q ~(p ~q)~ p (~(~q))~p q p (~p q)p q

9 Chapter 01 9 p (~p q)(p ~p) (p q)f (p q)p q T F F T (duality) p ( qr) ( pq) ( pr) p ( qr) ( pq) ( pr ) p T p T F p F p 7 p (~ pq) pq p (~ pq) pq (1) ( p q) ~ ( F q ) (2) ~( p qr) ~( T q )

10 10 (1) ( p q) ~( F q) ( p q) ~( T q ) (2) ~ ( p qr) ~ ( T q) ~( p qr) ~( F q )

11 Chapter A (14) 1. p (~p q) 2. ~[~(~p)] 3. ~[p (~q p)] 4. ~[~ p ~(p ~q) 5. p, q, r p, r q (1)~p (q ~r)(2)(p q) (~p r)(3)p (q r) 6. (1)( p q) (~ pq) ( p~ q) ( p~ q ) (2)( p qf) (~ pq) ( T p ) 7. (1) p ( pq) (2) ~ p ( p~ q) 8. (1) (2) (3) (4) 132 (5) (1) p p (2) p ~ q

12 (conditional proposition)p, q p q(if p then q) pq p (antecedent)q (concequent) pq p q pq T T T F T T T F F F F T pq (2) (1) 1+5=6 (3) 1+5=6 (2) 1+5=4 (4) 1+5=4

13 Chapter p q p q p q p q p q T T T T T F T T F F T F T F F F F F T F (1) p q pq (2) ~p q (3) ~q~p

14 14 pq~p q~q~p p(qp) p(qp)~p (~q p)~p (p ~q)(~p p) ~q T ~qt (pq)qp q (pq)q~(~p q) q(p ~q) q (p q) (~q q)(p q) Tp q

15 Chapter p qif and only if p then q p q p iff q (biconditional proposition) p q p q p q T T T F T F T F F F F T p, q p q p q pq qp p (p q)~p qpq p (p q) ( ) ~ ( ) p p q ( p q) p p p q ~( p q) p [(~ p p) (~p q)] [(~p ~q) p] [T (~p q)] [(~p ~q) p] (~ p q) [~q (~p p)] (~p q) [~ q T] (~p q) T ~p q pq

16 16 p q p(p q) ~p q pq T T T T F T T F T T F T T T T F F F F F F F F T F T T T pq p q (converse) qp(inverse)~p~q (contrapositive) ~ q~ p

17 Chapter pq5+2=8 (1) pq 5+2=8 (2) qp 5+2=8 (3) ~p~q 5+28 (4) ~ q ~ p (1) p q x>2 x 3 8 p q q ~q p ~ p a, b k ab a k b k p 1 a k p 2 b k ~(p 1 p 2 )~p 1 ~p 2 p 1 p 2 ~(~p 1 ~p 2 ) ~p 1 a> k ~ p 2 b> k

18 18 a> k b> k ab> k k =k ab k ab k a k b k

19 Chapter B 1. (1) p (pq)7 (2) ~p(pq) (3) p[q(p q)] 2. pqr (1) (2) (3) (4) 3. (1) (pq) (rq)(p r)q (2) p(q r)(p ~q)r 4. (1) (pq)qp q (2) p(q r)(pq)(pr) 5. m>2 n>2 m+n>mnm, n 6. p ( q~ r) 7. ( p~ q) ~ r

20 20 8. a 1, a 2,, a 5 a 1 a 2 a 5 13 aa 1 2 a 5 6 a, a a ABC A B C B ab, a 3 b 3 3 a b 1

Chapter 1 選用好的燜燒罐選用好的燜燒罐是做好燜燒罐料理最重要的步驟, 除了須注意使用的材質是否符合食器使用標準, 也須注意燜燒罐的保溫效果, 才能安心享用燜燒罐

Chapter 1 選用好的燜燒罐選用好的燜燒罐是做好燜燒罐料理最重要的步驟, 除了須注意使用的材質是否符合食器使用標準, 也須注意燜燒罐的保溫效果, 才能安心享用燜燒罐作者序不僅吃得好, 瘦身成效更好在學校指導學生飲食控制的時候, 發現外宿的學生不能自己開伙, 只能吃學生餐廳或在校外隨便吃一般學生餐廳提供的自助餐, 相較於其他餐點較為天然健康便宜, 但是學生多, 常常去得晚了就沒菜了,