1. F F (PAT 1)
1. F p, q, r F F F
. F ⇒( ⇒( ∨ )) F ⇒( ∨ )
. F ∧( ⇒ ) F ( ⇒ )∨∼ ( ⇒ ∼ )
F F
1. . . 2. . .
3. . . 4. . .
2. F F = {{ } { } { }}
F F
1. ∀ ∀ [ ∩ ≠ ∅] 2. ∀ ∀ [ ∪ = ]
3. ∀ ∃ [ ≠ ∧ ⊂ ] 4. ∃ ∀ [ ≠ ∧ ⊂ ]
3. F = {∅ { }}
F F
1. ∅ ⊂ 2. {∅} ⊂
3. { { }} ⊂ 4. {{ } { { }}} ⊂
4. F = { F ≤ }
= { ∈ 3 x }
P(B) F F F
1. 2.
3. 4.
5. F = { = } F F F S
1. { = } 2. { = }
3. { = − } 4. { = }
6. FS − + − =
S F F F
1. 2.1 2. 2.2
3. 3.3 4. 3.5
1

2. 7. F = { − ≤ − } a F A
F a F F F
1. (0, 0.5] 2. (0.5, 1]
3. (1, 1.5] 4. (1.5, 2]
 ≥
8. F ( )= − − ( ) = 
− <
F − ( ( ) + (− )) F F F
− +
1. 2.
− +
3. −
4. −
9. F = [− − ]∪[ ] = {( )∈ × − = − }
F > ∈ ∈ F + F F F
1. 2.5 2. 3
3. 3.5 4. 4
10. F ( ) = − ∈ (−∞ − ] ∪ [ ]
( ) = ∈ (−∞ ]
F F
1. ⊂ 2. ⊂
3. f F − 4. g F F −
11. F θ− θ = F F θ F F F
1. 2.
3. 4.
12. F ABC A F = =
F ( ) F F F
1. 2.
3. 4.
2

3. 13. F − ≤ ≤
π
− =
F F ( π ) F F F
1. 2x 2. −
3. − 4. −
14. F = { F = F = + }
= { F = + = − }
{ = ∈ − } F F F
F
1. (0, 1) 2. (0, 2)
3. (1, 2) 4. (0, 4)
15. F F F − + = F
F (a, b) F + F F F F
1. 4 2. 5
3. 6 4. 7
16. F F F (2, 1) F F =
F F F F F F
1. (0, 1) 2. (0, 2)
3. (1, 0) 4. (3, 0)
17. F F (± ) F ( ) F F
F
1. (− ) 2. ( )
3. (6, 0) 4. ( − )
18. F − = + = F F y F F F
1. − 2. −
3. 1 4. 2
3

4. 19. = + F F F
1. [0, 4) 2. [4, 8)
3. [8, 12) 4. [12, 16)
20.   +  = F F
   
. F a F >
. F F F
F F
1. . . 2. . .
3. . . 4. . .
 − 
 
21. F =   x y
 
 
F ( ) = ( ) = F ( ) F F F F
1. − 2. −
3. 30 4. 33
− 
 
22. F =  −  2 3 − F
 
 
F F
1. − 2. −
3. 4. 2
23. F x, y, z F
− − = −
− + = −
− + − =
F F
1. + + = 2. + + =
3. = 4. = −
4

5. 24. F ABCD F M F AD =
N F AC = F = + F
+ F F F
1. 2.
3. 4. 1
25. F F F
F F + F + F ⋅ F F F
1. − 2. 0
3. 4.
26. FS + + =
z F F F F S
1. {− − + }
2. { + − + }
3. {− − − + }
4. { + − − }
27. F F + = − =
F + F F F
1. 1 2. 2
3. 3 4. 4
28. F C F F x y F F = +
x, y + ≥ + ≥ ≥ ≥ F F
C F F F F F F
1. 2.
3. 4.
∞
29. F +
= F Σ 


 F F F
→∞ − = +
1. 2.
3. 1 4. F F F
5

6. 30. F F +
= n
F Σ = F Σ F F F
= =
1. − 2. −
3. − 4. −
∞
31. F Σ = F F F
=
F F F
1. 4
2. 2
3. 1
4. F F F F F F F
32. F
A F F F F = − X
B F F F = X = −
=
F c F = F F F
1. 2. 2
3. 4. 4
33. F ( ) = − + f F F F
1. (− − )∪( ) 2. (− − )∪( )
3. (− )∪( ) 4. (− )∪( )
  ( + )− ( )
34. F ( ) =  +  F F ( + )− ( )
F F F
  →
1. 1 2.
3. 4.
35. F = { } = { }
= { → F } F F F
1. 12 2. 24
3. 36 4. 39
6

7. 36. 4 F F
F F 8 F
F F F
F F F F
1. 96 2. 192
3. 288 4. 384
37. F F F F 4 F F3 F
F 2 F 1 F F 4 F
FF F F F
1. 2.
3. 4.
38. 7 F F F
F 3 F3 F F 2
F F F F F
F F F
F F F
1. 2.
3. 4.
39. Fn F n F {1, 2, ...,
2n} F F F F F F F F F
1 F F F
1. 2.
3. 4.
40. F 99 F F F F
F F F F F
1. Σ = Σ 2. Σ ( − ) = Σ ( − )
= = = =
3. Σ − = Σ − 4. Σ ( − ) = Σ ( − )
= = = =
7

8. 41. F 80
( ) 3.5 4 4.5 5 5.5 6
( ) a 15 10 20 b 5
F F F 4.5 F F F F
F F
1. 2.
3. 4.
42. F 40
( )
9 - 11 15
12 - 14 5
15 - 17 5
18 - 20 10
21 - 23 5
F F F F F F
1. = F F
2. = F F
3. = F
4. = F
43. F F F a, b, c, d F
F FF
F a b c d
F (z) -3 -0.45 0.45 1
F F
1. − + + − = 2. − + + − =
3. − + + = 4. − + − =
8

9. 44. F .6 F F
F F 140.6 F 3.01%
F F F F F 159.4 F 46.99% F
F F F 155 F F 160 F F
F F F F F F F 0
z
z 1.00 1.12 1.88 2.00
F F F 0.3413 0.3686 0.4699 0.4772
1. 12.86 % 2. 13.14 %
3. 15.87 % 4. 13.59 %
45. F F F F (X)
F (Y) 100 F F F F F
F F F = +
Σ = Σ = Σ = Σ =
= = = =
F F F 15 F
F( ) F F F
1. 16 2. 16.67
3. 17 4. 17.67
46.
1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, ...
F 5060 F F F F
1. 1 2. 10
3. 100 4. 1000
47. Fn r F 11
F F F r F F
1. 1 2. 3
3. 5 4. 7
9

10. 48. F P(x) Q(x) 2551 F ( ) = ( )
= ( ) = ( )+ F ( )− ( ) F
F F
1. 0
2. 1
3. −
4. F F F F
49. 6 , , , , F
F F
F F
F 4
F F F F 5 F F
F F
1. 2.
3. 4.
50. FF F F F
1. F 2 2. F 3
3. F 4. F
********************
10

11. F F F
PAT 1 / . . 52
F 1 2
. → ( → ( ∨ )) ≡ ∼ ∨ (∼ ∨ ( ∨ ))
≡ ∼ ∨∼ ∨ ∨
≡ ∼ ∨( ∨ )
≡ →( ∨ )
. ∧( → ) ≡ ∧ (∼ ∨ )
≡ ( ∧∼ ) ∨ ( ∧ )
≡ ( ∧∼ )∨∼ (∼ ∨∼ )
≡ (∼ ∧ )∨∼ ( → ∼ ) ∗
* ∼ ∧ ≡ ∼ ∨ ≡ →
F 2 1
1 F F
2 F { }∪{ } = { } ≠
3 F = { } F F y F ≠ ∧ ⊂
( F { } { } { })
4 F x F ≠ ∧ ⊂ ∈
F 3 2
1. ∅
2. ∅ ∈ ∴ {∅} ⊂
3. { }∈ ∴ { { }} ⊂
(F F F )
4. { }∈ F { { }} ∉
{{ } { { }}} ⊂
11

12. F F F
F 4 1
= { }
= { }
∴ ( ) =
∴ ( ) = ( ) =
F 5 2
= F = → = −
F 1 = → =
F 2 = → = −
F 3 = − → = −
F 4 = → − = → ( − ) = → =
F F 2 F
F 6 4
− + − =
F − + − =
−−  =
  =
F 7 4
− ≤ −
F −( − ) ≤ − − ≤ −
− + ≤ − ≤
− ≤ ≤
REAL ∩ (−∞ ]
F (−∞ ]
F 2
12

13. F F F
F 8 1
+
( ) = − → − ( ) =
 ≥
g(2) =  → = ≥
− <
→ = − ∴ ( ) =
 ≥
(− ) − =  → − = − <
− <
→ = < → = − ∴ (− ) = −
− ( ( ) + (− )) = − ( + (− ))
− +
= − (− ) =
F 9 2
∈ ∴ − ≤ ≤ − ≤ ≤ ( )
r; − = − → = +
(1) ; − + ≤ + ≤ − + + ≤ + ≤ +
− ≤ ≤ ≤ ≤ ( )
F ∈ ∴ (2) ∩ F = −
y = + F = −
∴ = {− } = {− } > ∴ + = + =
2 F = + ∈ [− − ]∪[ ]
y F = {( ) (− − )}
= =
2
∴ + =
1
x
-2 -1 1 2
-1
-2
13

14. F F F
F 10 1
( ) = − = (−∞ − ] ∪ [ ]
y f F F − ( 3 )
F x
2 (− ) (1, 0)
x
-1 1
-1
( ) = = (−∞ ]
y g F −
y = 2x
( 4 )
1
x
2 F = [− ∞) = ( ]
2 F 1 ⊂
F 11 3
θ− θ = → θ− θ θ+ θ =
θ θ = − ∴ θ =
F 12 4
F
C e F = → =
 
1 6 ∴ = − = − 



=
60
A B
14

15. F F F
F 13 2
π
= −
π
= ( − )
π
= (π − − ) + = π
π
= (π − ) = ( )
π
= − ( ) = −
F 14 3
= { / F = F = + }
F = ( ) = + ( )
F y (1) (2) F ( ) = +
− = → ( − ) = → = ±
−
F = F = + F x F F F
− ≤ → ( − )( + ) ≤
-1 1
∴ A F F [− ] F =
= { F = + = − }
= + → − + = F 2
CP <
− +
p <
+
C(0,0) <
y2= 1 - x 2
x2 + y 2 = 1 − < <
∴ B F F (− )
∈ − = (− − )∪( )
= = ( )
15

16. F F F
F 15 3
PARA − + =
− + = − +
( − ) = − ( − ) F (1, 2)
C
c=1 (a,b) = (2,b) → =
=
B(1,2)
A(0,0) − −
−
= −
=
DI : x=2
∴ + = + =
F 16 1
l ml = 1 CP
3
P(1,b) CP 1 = = ( + − ) +( − ) =
= −
C(2,1) −
= − ( − ) +( − ) =
−
F = + (0, 1)
= F (0, 1)
F x = F
F 17 1
P(2, 21 )
2
= +
F1 (-3,0) F2 (3,0) 2a = ( + ) +( − ) + ( − ) +( − )
2a = → =
= = → =
= + → = + → =
F + =
(− ) F (− ) F
16

17. F F F
F 18 2
− = → − =
F − = ( )
+ = → + =
F + = ( )
(1) (2) F = −
F 19 3
= +
F = +
= +
( ) = +
( ) − − =
( − )( + ) =
F = = −
= = −
= =
F =
= + = =
F 20 3
  + 
    = 1
F + = 1
+ =
F F = F
F a F = ..... F ( )
  +  =
   
17

18. F F F
F   F   F F
   
  +  = F ..... F ( )
   
F 21 4
( ) = 13 ( ) = 9
F ( ) = 13 F − ( ) = 9
−
−
= 13 − = 9
xy
− = 13 ( ) −( + ) = 9
y = −
F y (1)
F (− )− = 13
x = −
− − + = +
 −  −
 
=  −  = − − = + + = +
 
 −  −
+ + − = +
F 22 3
−  − 
   
=  −  → =  −  F F =
   
   
−
= ( )
−
= ( ) = [− ( )]
0
−
−
= − = − (− + ) =
−
18

19. F F F
F 23 1
− − = − ( )
− + = − ( )
− + − = 4 ( )
( )+( ) F − = − → =
( )+( ) F − = − ( )
F y (4) F − ( ) = − → =−
F x y F (3) F −(− ) + − = → =−
1 + + = (− ) + + (− ) =
2 + + = − + + (− ) = −
3 = (− )( )(− ) =
(− )( )
4 = −
=
F 24 1
= −
D C
= −
4
= ( + )−
M 5
1 = −
N
1
A B ∴ + = − = −
= =
F 25 1
( + )⋅( + ) = 0
+ + ⋅ = 0
+ + ⋅ = 0
⋅ = −
F 26 4
+ + =
− ± − − ±
= = = − + − −
= + − −
19

20. F F F
F 27 3
F vector
+ = + ⋅ + ( )
− = − ⋅ + ( )
( )+( ) + + − =  + 
 
z vector F
+ + − =  + 
 
+ =  + 
 
∴ + =
F 28 2
F = +
F
+ ≥ 5
+ ≥ 3
x ≥ 0
y ≥ 0
F intersect F
y
(0, 5 )
4
(0, 1)
( 3,5 )
5
4
5
x
( 3 , 0) (3, 0)
3x + 4y = 5 x + 3y = 3
F F
( ) = ( )+ ( ) =
( ) = ( )+ ( ) = F C
( ) = ( )+ ( ) = 9
20

21. F F F
F 29 2
+
= → = → =
→∞ −
∞ ∞ ∞
∴ Σ   = Σ   = Σ  
=  +  =  +  =  
= +  +  +
   
= =
−
F 30 2
+
= F =
Σ = → ( + + + )+( + + + )=
=
( − ) ( − )
−
+ −
= → + =
Σ = ( + + + )+( + + + )
=
( − ) ( − )
= −
+ −
= − ( + )= −
F 31 3
∞
Σ = 4 → + + + =
=
−
= 4 → = ( − ) → = ( − )
= −
∴ F = (− )( ) −
(− )
=
F 32 2
A
y = ( )( ) = F
1
-1 1
x
y = 1 - x2
21

22. F F F
B
y 2 B = ∫ 
  =
y = x4 −  −
= − − 
  =
x
-C C
FF F = F =
=8 ∴ =
F 33 3
f F ( )>
( ) = − >
( − )>
( − )( + )>
3 0 3
2 2
4 F F F 3 (− )∪( )
F F F ( )>
F 34 2
( + )− ( )
= ( )
→
( + )− ( )
( + )− ( ) →
=
→ ( + )− ( ) ( + )− ( )
→
 + 
( )  
= ( )
=
 + 
= =
 
22

23. F F F
F 35 3
={ } ={ }
F F A B = × =
F F F
→∆
→∆
→∆
0
F 36 1
F
F
F
F F ( ) =
F F
F 37 1
n(S) = F 4 10
=  
 
= 210
n(E) = F 4 F
=  
 
  
  
= 24
F P(E) = =
23

24. F F F
F 38 1
n(S) = 7 F F =    
   
= 210
n(E) = 7 F F F F
F 3
F F F
F * =    
   
F * =  
 


= 40
F ( )= =
F 39 3
 
 
P( F F ) =  
=
 
F   =
 
F n = 3
F {1, 2, 3, 4, 5, 6}
F   
  
P( F F 1 )=  
 
=
F 40 3
F FF F F F 3 F F
F F F F ( )
24

25. F F F
F 41 4
µ= Σ
( ) + ( )( ) + ( )( ) + ( )( ) + ( ) + ( )( )
=
F + = 250 ................. (1)
+ + = 80
+ = 30 ................. (2)
(1) (2) F = =
F (MD) = Σ −µ
FF F µ=
MD = ( )( ) + ( )( ) + ( )( ) + ( )( ) + ( )( ) + ( )( )
=
F 42 4
.( ) (f) d fd
9 - 11 15 0 0
12 - 14 5 1 5
15 - 17 5 2 10
18 - 20 10 3 30
21 - 23 5 4 20
40 65
Σ
µ = +
µ = + ( )( )
= 14.875
25

26. F F F
.( ) (f)
9 - 11 15 F
12 - 14 5 F
15 - 17 5
18 - 20 10
21 - 23 5
F F F
F = F F
F 43 1
−µ
= σ
−µ
FF − = σ → = µ− σ
−µ
− = σ → = µ− σ
−µ
0.45 = σ → = µ+ σ
−µ
1 = σ → = µ+σ
a, b, c d F F F 1
F 44 4
F F
3.01% .4699 46.99%
140.6 159.4
z = -1.88 z = 1.88
−µ
F − = σ .................. (1)
−µ
1.88 = σ .................. (2)
26

27. F F F
(1) (2) F µ= σ=
= −
=
= −
=
.4772 - .3413 = .1359
13.59%
z1 = 1 z2 = 2
F 45 2
= +
Σ = Σ +Σ → = + ............. (1)
Σ = Σ + Σ → = + ............. (2)
(1) (2) F =− =
F =− +
F = F =− + ( )= =
F 46 2
F = = = = =
F ( + )
=
F = F =
∴ = = =
27

28. F F F
F 47 4
n F 11
1 1 1
2 4 4
3 9 9
4 16 5
5 25 3
.
. .
. .
.
. . .
.
. .
. .
.
. . .
F F 11 7 F F
F 48 3
( ) = ( )− ( )
( )= ( ) =
FF ( )− ( ) = =
F ( ) = =
∴ ( ) = ( − )( − )( − ) ( − ) ( )
F ( ) = ( )+ → ( )− ( ) = → ( ) =
∴ (1) =
( ) = ( − )( − )( − ) ( − )
= ( )( )( ) ( )→ =
∴ ( )− ( ) = ( ) = ( − )( − )( − ) ( − )
= ⋅ (− ) = −
28

29. F F F
F 49 3
(1) F 4
F F
F F
, ,
F
.... F 3
F 50 3
************************
29