1. ก 1 ก
! " #
1 " $"
1. &' p , q , r ,$ $ p→q - . ,$ / 0 1 q ∨ r - . ,$
/ .1 .' . . $ [~ q ∧ ( p ∨ r )] ↔~ r
2. &' p , q , r ,$ $5 [( p ∧ q ) ∧ r ] → ( p ∧ s ) - . ,$ 0
67 p , q , r 67 s - . ,$ .9
3 . 7.&$; . .&'5<ก .
1) p∧q ≡ ....................................
2) p∨q ≡ ....................................
3) p ∧ ( q ∧ r ) ≡ ....................................
4) p ∨ ( q ∨ r) ≡ ...................................
5) p ∧ ( q ∨ r ) ≡ ....................................
6) p ∨ ( q ∧ r ) ≡ ....................................
7) ~( p ∧ q ) ≡ ....................................
8) ~( p ∨ q ) ≡ ....................................
4. ก
1) p → q ≡ ....................................
2) ~( p → q ) ≡ ....................................
3) p → q ≡ ....................................
4) p ↔ q ≡ ....................................

2. ก 2 ก
! " #
" $" &'$"ก - $6 . D-
1. !"#$ % &! '( ) ก* "+ & ( p → q ) ∧ ( p → r ) ก*- p → ( q ∧ r )
D-
2. !"#$ % &! '( !. )* "* /"% "+ & ( p ∧ q ) → ( p ∨ q )
D-
3. !"#$ % &! '( !. )* "* /"% "+ & [ p → (~q) ] ∨ [ q → (~p) ]
D-
4. " ) - ก" 01 &! '() 01 "+ &
' # 1. p → q 2. ~p → ~ r
3. s → r 4. ~q
F7 ~s
5. 0 1. ก $- $ก "4'56 7 8 "'5 9 ก #:+( 8 "'5
2. ก & &/:+( 8 "'5
1 ก & $- $ก "4'56 7 8 "'5

3. ก 3 ก
! " #
" $" &'$"ก - $6 . D-
1.ก / U = { x | x !. 8 - ก4'5 7ก 10 }
" 6 ∃ x [ (x > 4 ) ∧ (x < 7) ]
2. ก / U = {G1 , 0 , 1} "6
(1) ∃ x ∀ y [ x ≤ y ] (2) ∃ x ∀ y [ x + y = 0 ]
3. )K6 6 ∃ x ∀ y [ ( xy < 0 ) → ( x < 0 ∨ y < 0 ) ] + 6 6 /
4. )K6 6 ∃ x [ P(x) ∧ ~Q(x) ] + 6 6 /

4. ก ก7 .G 1/54
! " #
#9
I . - $J ก .
6 )- N O ) "% $5 1 31201
) "*- *ก "'7 *( *K7 OPกQ !R4'5 4 S "'7 4'5 1 !Rก "OPกQ 2554
) - * 4'5 22 ก"กT $.O. 2554 10.40 – 12.10 .
+5 ……………………………. )ก0 ………………………….. *( ....../......... 64'5 ......
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6 ) - '4*( / 10 6 *ก "'7 9)/ K'4 40ก6
1) 6 4'5) ก*-6 /5 $K "$ <. LK$ 67 M"$ NO$ "ก $ I . - $1 + 6 /
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2) $ D6 ∃ x [ P(x) ∨ ∼Q(x) ] + 6 /
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3) $ D6 6 ∀ x [ x > 0 → x2 > 0 ] + 6 #&"
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4) ∀ x [ 3x > 12 ] , µ = {0 , 4 , 5 , 6} ' " !. #&"
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5. 5) ∀ x ∃ y [ x < y ] , µ = I ' " !. #&"
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6) 6 &! '( !. " ) -* 6 "6 /
( ) -* !V/) "*-ก "- ก ), ( ) -* !V/) "*-ก " N ), ( ก ") *-4'5) "*-ก "- ก ),
( ก ") *-4'5) "*-ก " N ), ( ก " ! '57 ) "*-ก "- ก ), ( ก " ! '57 ) "*-ก " N ),
( ก " ' ก *กQN%ก "- ก ) ( ก " ' ก *กQN%ก " N ) ( ก " ' "%)ก "- ก ) (
ก" ' "%)ก " N ) ( ก "9 ก9 )
6.1) q ⋅ 37 = 37 ⋅ q ………………………………….
6.2) (2 + 3) p = 2 p + 3 p ………………………………….
6.3) 6 + (5 + y) = (6 + 5) + y ………………………………….
6.4) (2 + 3)(5 + 6) = (5 + 6)(2 + 3) …………………………………
6.5) 3 + (4 + 6) = 3 + (6 + 4) ……………………………
6.6) a (b+ c) = (b + c) a ………………………………….
6.7) –5 + π !. " ……………………………
6.8) ' " 4'5- กก*- –15 9 &/ 0 ………………………………….
6.9) 1 x 1 = 1 ………………………………….
7) .' P '7 +5 " x3 – 7x2 + 11x – 4 / 7 x – 3
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8) .' a 4'54 x – 3 " 3x3 – 7x2 – 9x – a " *
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6. 9) .' 6 ) ก " x3 + x2 – 8x – 12 = 0
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10) 9ก) ก " x &! '( x3 – 10x2 + 27x = 18
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#7 "$D