Chapter 01 1.1 1.2 1.3 1.4
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
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 (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
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 ~[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
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 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
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 (1) ( p q) ~( F q) ( p q) ~( T q ) (2) ~ ( p qr) ~ ( T q) ~( p qr) ~( F q )
Chapter 01 11 1 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) 112 23 4 (2) 112 23 5 (3) 125 23 4 (4) 132 (5) 2 3 5 9. (1) p p (2) p ~ q
12 1.2 (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
Chapter 01 13 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 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
Chapter 01 15 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 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
Chapter 01 17 pq5+2=8 (1) pq 5+2=8 (2) qp 5+2=8 (3) ~p~q 5+28 (4) ~ q ~ p5 2 8 6 (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 a> k b> k ab> k k =k ab k ab k a k b k
Chapter 01 19 1 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 8. a 1, a 2,, a 5 a 1 a 2 a 5 13 aa 1 2 a 5 6 a, a a 1 1 2 5 9. ABC A B C B 45 10. ab, a 3 b 3 3 a b 1