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2010 2010

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<ul><li><p> (2)_______________________________ 2010 </p><p> { } 1 A B 1) A 2) B *3) A 4) B n(A) A 1. n(U) = n(A) + n(A) 2. n(AU B) = n(A) + n(B) - n(AI B) 3. n(AU BU C) = n(A) + n(B) + n(C) - n(AI B) - n(AI C) - n(BI C) + n(AI BI C) 4. n(A - B) = n(A) - n(AI B) </p></li><li><p> 2010 _______________________________ (3) </p><p> 2 </p><p> AU B AU C BU C AU BU C AI BI C 25 27 26 30 7 </p><p> (AI B)U C *1) 23 2) 24 3) 25 4) 26 3 46 </p><p> 39 19 </p><p> 1) 9 2) 10 3) 11 *4) 12 4 50 32 6 </p><p> 1 </p><p> *1) 11 2) 12 3) 17 4) 18 5 A B n(AU B) = 88 n[(A - B)U (B - A)] = 76 </p><p> n(A) = 45 n(B) 1) 45 2) 48 3) 53 *4) 55 </p></li><li><p> (4)_______________________________ 2010 </p><p> 6 300 100 100 150 ( 50 ) </p><p> A B A B </p><p> A B 7 A = {1, 2} B = {1, 2, 3, 4, 5} A </p><p> B A B A A P(A) 8 A = {1, 2, 3} A , {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3} P(A) = {, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} 1. 2. 3. A A 4. A P(A) 5. A B P(A) P(B) 6. A 2n(A) 7. P(A) 2n(A) </p></li><li><p> 2010 _______________________________ (5) </p><p> 1. A B A B AU B 2. A B A B AI B 3. A B A B A - B 4. A U A U A A 9 U = {1, 2, 3, ..., 10} A = {1, 2, 4, 8} B = {2, 4, 6, 10} AU B = {1, 2, 4, 6, 8, 10} AI B = {2, 4} A - B = {1, 8} B - A = {6, 10} A = {3, 5, 6, 7, 9, 10} B = {1, 3, 5, 7, 8, 9} 10 A - B = {2, 4, 6}, B - A = {0, 1, 3} AU B = {0, 1, 2, 3, 4, 5, 6, 7, 8} AI B 1) {0, 1, 4, 5, 6, 7} 2) {1, 2, 4, 5, 6, 8} *3) {0, 1, 3, 5, 7, 8} 4) {0, 2, 4, 5, 6, 8} </p></li><li><p> (6)_______________________________ 2010 </p><p> 2 1. (Inductive Reasoning) 2. (Deductive Reasoning) 1 1) 1. 2. 2) 1. 2. 2 a 1, 4, 9, 16, 25, a 2, 4, 8, 16, 32, a - 1. a A 2. a A </p></li><li><p> 2010 _______________________________ (7) </p><p> 3. A B 4. A B 5. A B 6. A B 3 . . *1) 2) 3) 4) 4 1. 2. 300 3. 300 1) 2) *3) 4) </p></li><li><p> (8)_______________________________ 2010 </p><p> 5 </p><p>1 2 47</p><p>2 4 814</p><p>3 6 1221</p><p>. . . a b c77</p><p> 2a - b + c 1) 11 2) 22 3) 33 *4) 44 6 . . . 1) 2) </p><p> 3) *4) </p><p> 7 1. 2. 3. 1) *2) 3) 4) </p></li><li><p> 2010 _______________________________ (9) </p><p> (R)</p><p> (Q) (Q)</p><p> (I) (I)</p><p> (I-) (I0)</p><p> (I+) () (N) </p><p> 2 , 5 , - 3 , , 2.17254... 1 . 0 . 0 1) . . 2) . . 3) . . *4) . . 2 3 3 5 1.732 </p><p>2.236 . 2.235 + 1.731 5 + 3 2.237 + 1.733 . 2.235 - 1.731 5 - 3 2.237 - 1.733 *1) . . 2) . . 3) . . 4) . . </p></li><li><p> (10)______________________________ 2010 </p><p> 1. a, b, c R 1) a = a 2) a = b b = a 3) a = b b = c a = c 4) a = b a + c = b + c 5) a = b a + c = b + c 2. a, b, c R </p><p> a + b R a b R a + b = b + a a b = b a a + (b + c) = (a + b) + c a (b c) = (a b) c 0 </p><p> 0 + a = a = a + 0 1 1 a = a = a 1 </p><p> a -a (-a) + a = 0 = a + (-a) </p><p> a a 0 a-1 a a-1 = a-1 a = 1 </p><p> a(b + c) = ab + ac 3 a b c d . a - b . c - d 1) . . *2) . . 3) . . 4) . . </p></li><li><p> 2010 ______________________________ (11) </p><p> 4 . b b + a = 0 = a + b . a b </p><p> ba = 1 = ab 1) . . *2) . . 3) . . 4) . . 1. (a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 - 2ab + b2 2. (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a - b)3 = a3 - 3a2b + 3a2b - b3 3. a2 - b2 = (a - b)(a + b) 4. a3 - b3 = (a - b)(a2 + ab + b2) a3 + b3 = (a + b)(a2 - ab + b2) ax2 + bx + c = 0 a, b c , a 0 x = 2a</p><p> 4ac b b 2 -- b2 - 4ac &gt; 0 x 2 b2 - 4ac = 0 x 1 b2 - 4ac &lt; 0 x </p></li><li><p> (12)______________________________ 2010 </p><p> a, b c 1. a &gt; b b &gt; c a &gt; c 2. a &gt; b a + c &gt; b + c 3. a &gt; b c &gt; 0 ac &gt; bc a &gt; b c &lt; 0 ac &lt; bc 4. a b a &lt; x &lt; b a &lt; x x &lt; b a b a &lt; b 1. (a, b) = {x|a &lt; x &lt; b} a b 2. [a, b] = {x|a x b} a b 3. (a, b] = {x|a &lt; x b} a b 4. [a, b) = {x|a x &lt; b} a b 5. (-, a) = {x|x &lt; a} a 6. [a, ) = {x|x a} a 5 65 </p><p> 3 1) 30 *2) 36 3) 42 4) 48 </p></li><li><p> 2010 ______________________________ (13) </p><p> 6 y = ax2 + bx + c a 0 ax2 + bx + c = 0 </p><p> 1) </p><p>y</p><p>x50</p><p>5</p><p>-5</p><p>-5</p><p> 2) </p><p>y</p><p>x50</p><p>5</p><p>-5</p><p>-5</p><p> 3) </p><p>y</p><p>x50</p><p>5</p><p>-5</p><p>-5</p><p> *4) </p><p>y</p><p>x50</p><p>5</p><p>-5</p><p>-5</p><p> 7 1 3 4 </p><p> 100 250 50 100 100 20% </p><p> 1) 10 *2) 12 3) 14 4) 16 </p></li><li><p> (14)______________________________ 2010 </p><p> 8 -1 2 + 21</p><p>x-</p><p> 1 1) [ 2 - 1, 1] 2) [ 2 - 1, 2] *3) [3 - 2 2 , 1] 4) [3 - 2 2 , 2] a |a| = </p><p> a x &lt; -a x &gt; a |x| a x -a x a 9 |x - 7| = 6 1) 10 15 2) 14 *3) 2 4) 3 </p></li><li><p> 2010 ______________________________ (15) </p><p> 10 </p><p> += 0 a a1 |a| |a|1 a x x22</p><p>--</p><p> 1) 1 *2) 2 3) 3 4) 4 </p><p> 11 x3 - 2x = |x| 1) 0 2) 3 *3) 3 - 1 4) 3 + 1 </p></li><li><p> (16)______________________________ 2010 </p><p> A B A B A B = {(a, b)|a A b B} A = {1, 2} B = {a, b, c} A B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} B A = {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)} A, B C 1. A = A = 2. A B B A 3. n(A B) = n(A) n(B) 4. A (BU C) = (A B)U (A C) (BU C) A = (B A)U (C A) 5. A (BI C) = (A B)I (A C) (BI C) A = (B A)I (C A) 1 A = {1, 2} B = {a, b} A B * 1) (2, b) 2) (b, a) 3) (a, 1) 4) (1, 2) A B r A B r A B r A r A A * A B 2n(A)n(B) </p></li><li><p> 2010 ______________________________ (17) </p><p> 2 A = {1, 2, 3, 4, 5, 6} B = {1, 2, 3, ... , 11, 12} S = </p><p> += 2a 2a b B A b)(a, </p><p> S 1) 1 * 2) 2 3) 3 4) 4 3 A = {1, 2, 3, 4} r = {(m, n) A A | m n} r </p><p> 1) 8 * 2) 10 3) 12 4) 16 r Dr r </p><p>Dr = {x|(x, y) r} r Rr r </p><p>Rr = {y|(x, y) r} r = {(-2, 4), (-1, 1), (1, 1)} Dr = {-2, -1, 1} Rr = {1, 4} r R R 1. y x x </p><p> y 2. x y y r (x, y) r (x, z) r y = z r (x, y) r (x, z) r y z </p></li><li><p> (18)______________________________ 2010 </p><p> 1. r r 1 r r1 = {(a, 1), (b, 2), (b, 3), (c, 4)} r1 b 2 3 r2 = {(p, 2), (q, 4), (r, 6)} r2 2. r x x r 1 r x r </p><p> 1 r1 </p><p> x </p><p>r 1 r2 </p><p> 4 f = (x, y)|y = </p><p>2 3x xx</p><p>2 ++ + </p><p>1x12x </p><p>2 -- </p><p> 1) -2 2) -1 * 3) 0 4) 1 </p><p>y r1</p><p>x</p><p>y</p><p>r2</p><p>x</p></li><li><p> 2010 ______________________________ (19) </p><p> 5 A = {1, 99} A 1) 2) * 3) 4) 6 r </p><p>1 2</p><p>y</p><p>x30</p><p>123</p><p>-3 -2 -1</p><p>-3-2-1</p><p> 1) r (1, 1), (2, 2) (3, 3) 2) r * 3) r (3, 3) (3, -1) 4) r (1, 1) (-1, 1) (Linear Function) f(x) = ax + b a, b R (Constant Function) a = 0 X (Quadratic Function) f(x) = ax2 + bx + c a, b, c R a 0 a &gt; 0 a &lt; 0 f(x) = ax2 + bx + c a, b, c R </p><p>2ab f,2a</p><p>b -- </p><p>4a b 4ac ,2a</p><p>b 2-- </p><p> f(x) = a(x - h)2 + k a, k R a 0 (h, k) </p></li><li><p> (20)______________________________ 2010 </p><p> 1. x 2. y = a(x + c)2 c &gt; 0 x (-c, 0) x = -c y = a(x - c)2 c &gt; 0 x (c, 0) x = c 3. x x = 2a 4ac bb</p><p>2 -- (Exponential Function) y = ax a &gt; 0 a 1 (Absolute Value Function) y = |x - a| + c a, c R (Step Function) R 7 a y = a(2x) (3, 16) * 1) 2 2) 3 3) 4 4) 5 8 x y = -4x2 - 5x + 6 x * 1) </p><p>31 ,3</p><p>2 -- 2) </p><p>23 ,2</p><p>5 -- 3) </p><p>76 ,4</p><p>1 4) </p><p>23 ,2</p><p>1 </p><p> 9 a b y1 = 1 + ax y2 = 1 + bx </p><p>0x</p><p>1</p><p>2</p><p>yx</p><p>2 b 1 y +=x</p><p>1 a 1 y +=</p><p> 1) 1 &lt; a &lt; b 2) a &lt; 1 &lt; b * 3) b &lt; 1 &lt; a 4) b &lt; a &lt; 1 </p></li><li><p> 2010 ______________________________ (21) </p><p> 10 x = 3 f(x) = -x2 + (k + 5)x + (k2 - 10) k f </p><p> 1) -4 * 2) 0 3) 6 4) 14 11 f(x) = x2 - 2x - 15 1) f(x) -17 x 2) f(-3 - 2 - 3 ) &gt; 0 3) f(1 + 3 + 5 ) = f(1 - 3 - 5 ) * 4) f(-1 + 3 + 5 ) &gt; f(-1 - 3 - 5 ) </p></li><li><p> (22)______________________________ 2010 </p><p> a b m n k 1. am an = am+n 2. n</p><p>m</p><p>aa = am-n </p><p> 3. (am)n = amn 4. (am bn)k = amk bnk 5. </p><p>k</p><p>nm</p><p>ba </p><p> = nkmk</p><p>ba , b 0 </p><p> 6. a-n = na1 , a 0 </p><p> 7. a0 = 1, a 0 a n 1 a1/n = n a a m n 1 .. m n 1 n m a = am/n a b 1 m, n 1. am = an m = n 2. am = bm m = 0 a, b 0 </p><p> 1 22)(- + </p><p> +</p><p>3222 81/2 </p><p> 1) -1 2) 1 * 3) 3 4) 5 </p></li><li><p> 2010 ______________________________ (23) </p><p> 2 4</p><p>1258 </p><p> = </p><p>x/162516 </p><p> x </p><p> 1) 43 * 2) 3</p><p>2 3) 23 4) 3</p><p>4 3 1) (24)30 &lt; 220 330 440 2) (24)30 &lt; 230 320 440 * 3) 220 340 430 &lt; (24)30 4) 230 340 420 &lt; (24)30 4 ( 18 + 2 3 125- - 3 4 4 ) * 1) -10 2) 10 3) 2 5 - 5 2 4) 5 2 - 2 5 </p><p> 5 2</p><p>152 </p><p>65</p><p>- </p><p> * 1) 103 2) 10</p><p>7 3) 5 - 2 4) 6 - 2 </p></li><li><p> (24)______________________________ 2010 </p><p> a 1 m, n 1. am &lt; an a &gt; 1 m &lt; n 2. am &lt; an 0 &lt; a &lt; 1 m &gt; n 6 4(2x2-4x-5) 321 1) </p><p>25 ,2</p><p>5 - 2) </p><p> 1 ,25 - 3) </p><p> 1 ,2</p><p>1 - * 4) </p><p>25 ,2</p><p>1 - </p><p> 7 8x - 8(x+1) + 8(x+2) = 228 x 1) 3</p><p>1 * 2) 32 3) 3</p><p>4 4) 35 </p><p> 8 x383 3 + = 8116 x * 1) - 9</p><p>4 2) - 92 3) - 9</p><p>1 4) 91 </p><p> 9 1) 10 0.9 + &lt; 0.9 + 10 * 2) ( 0.9 )( 4 9.0 ) &lt; 0.9 3) ( 0.9 )( 3 1.1 ) &lt; ( 1.1 )( 3 9.0 ) 4) 300 125 &lt; 200 100 </p></li><li><p> 2010 ______________________________ (25) </p><p> 10 4a = 2 16-b = 41 a + b ( 0.75) </p><p> 11 x 2 (x2) = 4(4x)</p><p>42 </p><p> 1) 2 2) 3 * 3) 4 4) 5 12 1) 21000 &lt; 3600 &lt; 10300 2) 3600 &lt; 21000 &lt; 10300 * 3) 3600 &lt; 10300 &lt; 21000 4) 10300 &lt; 21000 &lt; 3600 </p><p> 13 35 </p><p>2732- + 3/2</p><p>6</p><p>(64)2 </p><p> * 1) - 2413 2) - 6</p><p>5 3) 32 4) 24</p><p>19 </p><p> 14 ( 2 + 8 + 18 + 32 )2 1) 60 2) 60 2 3) 100 2 * 4) 200 </p></li><li><p> (26)______________________________ 2010 </p><p> ABC BCA c a b ABC </p><p> a</p><p>A C</p><p>B</p><p>b</p><p>c c2 = a2 + b2 </p><p> ABC (sine) A = sin A = A </p><p> (cosine) A = cos A = A </p><p> (tangent) A = tan A = A A sin A = c</p><p>a , cos A = cb , tan A = b</p><p>a </p><p> 1. csc A = Asin</p><p>1 , sec A = Acos1 , cot A = Atan</p><p>1 </p><p> 2. tan A = AcosAsin , cot A = Asin</p><p>Acos </p><p> 3. sin2 A + cos2 A = 1 4. tan2 A + 1 = sec2 A 5. 1 + cot2 A = csc2 A </p><p>a</p><p>A C</p><p>B</p><p>b</p><p>c</p></li><li><p> 2010 ______________________________ (27) </p><p> A 90 - A </p><p>A B</p><p>C</p><p> sin A = cos (90 - A), csc A = sec (90 - A) cos A = sin (90 - A), sec A = csc (90 - A) tan A = cot (90 - A), cot A = tan (90 - A) 30, 45 60 </p><p> sin cos tan csc sec cot 30 21 2</p><p>3 31 2 3</p><p>2 3 </p><p>45 22 2</p><p>2 1 22 = 2 2</p><p>2 = 2 1 </p><p>60 23 2</p><p>1 3 32 2 3</p><p>1 </p><p> 360 = 2 180 = 90 = 2 60 = 3 45 = 4 30 = 6 1 * 1) sin 21 = cos 69 2) sin 21 = cos 21 3) cos 21 = tan 21 4) tan 21 = cos 69 </p><p>A 21 B</p><p>C</p></li><li><p> (28)______________________________ 2010 </p><p> 2 * 1) sin 30 &lt; sin 45 2) cos 30 &lt; cos 45 3) tan 45 &lt; cot 45 4) tan 60 &lt; cot 60 3 A B C </p><p> A B C </p><p> sin cos tan 40 0.643 40 0.766 40 0.839 41 0.656 41 0.755 41 0.869 42 0.669 42 0.743 42 0.900 </p><p> ABC B C 41 BX 1 AX </p><p> 1) A 2) B * 3) C 4) A, B C 4 1 </p><p> 1) 2</p><p>3 * 2) 332 3) 34 4) 23 </p><p>A C</p><p>B</p><p>X</p></li><li><p> 2010 ______________________________ (29) </p><p> 5 ABC C cos B = 32 BC 1 ABC </p><p> 1) 55 * 2) 4</p><p>5 3) 3</p><p>5 4) 25 </p><p> 6 ABCD 12 tan DBA = 31 AE BD E AE 1) 3</p><p>10 2) 5102 </p><p> 3) 210 * 4) 5</p><p>103 7 EFC , BAC , BEA </p><p> BDE 1) sin ( 1 ) = sin ( 5 ) 2) cos ( 3 ) = cos ( 5 ) * 3) sin ( 2 ) = cos ( 4 ) 4) cos ( 2 ) = sin ( 3 ) </p><p>C</p><p>F</p><p>A D B</p><p>E12 3 4</p><p>5</p></li><li><p> (30)______________________________ 2010 </p><p> (Sequences) n </p><p> n (Finite Sequences) (Infinite Sequences) (Arithmetic Sequences) n + 1 n </p><p> (Common difference) 1. a1 d d = an+1 - an n an = a1 + (n - 1)d 2. n a, a + d, a + 2d, ..., a + (n - 1)d 1 40 1) an = 1 - 2n 2) an = 1 + 2n * 3) an = 2 - 2n 4) an = 2 + 2n 2 31 - 201 , - 301 , - 601 , ... 1) 12</p><p>5 2) 3013 * 3) 20</p><p>9 4) 157 </p><p> 3 a1, a2, a3, ... a30 - a10 = 30 </p><p> 1) 1.25 * 2) 1.5 3) 1.75 4) 2.0 </p></li><li><p> 2010 ______________________________ (31) </p><p> (Geometric Sequences) n + 1 n </p><p> (Common ration) 1. a1 r r = n</p><p>na</p><p>1 a + n an = a1 rn-1 2. n a, ar, ar2, ..., arn-1 4 a1, a2, a3 a1 = 2 a3 = 200 a2 </p><p> * 1) -20 2) -50 3) 60 4) 100 5 a1, a2, a3, ... . a1 + a3 , a2 + a4 , a3 + a5 , ... . a1a2 , a2a3 , a3a4 , ... . </p><p>1a1 , </p><p>2a1 , </p><p>3a1 , ... </p><p> * 1) 2) 3) 4) 6 16 6251 , 5125</p><p>1 , 1251 , ... </p><p> 1) 25 5 2) 125 * 3) 125 5 4) 625 </p></li><li><p> (32)______________________________ 2010 </p><p> 7 * 1) an = 2n 32n 2) an = 2n + 4n 3) an = 3n2 4) an = (2n)n (Arinmetic Series) a1, a2, a3, ..., an a1 + a2 + a3 + ... + an Sn n S1 = a1 S2 = a1 + a2 S3 = a1 + a2 + a3 M M Sn = a1 + a2 + a3 + ... + an n Sn = 2</p><p>n [2a1 + (n - 1)d] Sn = 2n [a1 + an] 8 1 + 6 + 11 + 16 + ... + 101 1) 970 2) 1020 3) 1050 * 4) 1071 9 a1, a2, a3, ... a2 + a3 + ... + a9 = 100 S10 = a1 + a2 + ... + a10 1) 120 * 2) 125 3) 130 4) 135 </p></li><li><p> 2010 ______________________________ (33) </p><p> 10 S = {101, 102, 103, ... , 999} a S b S b - a </p><p> * 1) -550 2) -500 3) -450 4) 450 (Geometrics Series) a1, a2, a3, ..., an a1 + a2 + a3 + ... + an n Sn = r 1</p><p>)r (1a n1-- r 1 </p><p> 11 100 1) 1 + 3 + 5 + ... + (2n - 1) + ... + 199 2) 1 + 3</p><p>1 + 51 + ... + 1)(2n</p><p>1- + ... + 199</p><p>1 </p><p> 3) 1 + 2 + 4 + ... + (2n-1) + ... + 2199 </p><p> * 4) 51 + 125</p><p>1 + 31251 + ... + 12n5</p><p>1- + ... + 1995</p><p>1 </p><p> 12 1 - 2 + 4 - 8 + ... + 256 1) -171 2) -85 3) 85 * 4) 171 13 Sn n 2 S10 - S8 = 32 9 1) 3</p><p>16 2) 320 3) 3</p><p>26 * 4) 332 </p></li><li><p> (34)______________________________ 2010 </p><p> 1. k 1 n1 2 n2 3 n3 M M k nk n1 + n2 + n3 + ... + nk 2. k 1 n1 2 n2 3 n3 M M k nk n1 n2 n3 ... nk n 0 n! = n (n - 1) (n - 2) (n - 3) ... 3 2 1 5! = 5 4 3 2 1 8! = 8 7 6 5 4 3 2 1 * 0! = 1 1 1 </p><p>1 1 1 4 8 </p><p> 1) 168 2) 324 * 3) 672 4) 1344 </p></li><li><p> 2010 ______________________________ (35) </p><p> 2 A C B A B B C A C 1 </p><p> * 1) 5 2) 6 3) 8 4) 9 3 6 2 4 6 </p><p> 2 1) 12 2) 24 3) 36 * 4) 48 P(E) E P(E) = n(S)n(E) n(E) n(S) 1. 0 P(E) 1 2. P() = 0, P(S) = 1 3. P(E1U E2) = P(E1) + P(E2) - P(E1I E2) 4. P(E1U E2U E3) = P(E1) + P(E2) + P(E3) - P(E1I E2) - P(E1I E3) - P(E2I E3) + P(E1I E2I E3) 5. P(E) = 1 - P(E) P(E) </p></li><li><p> (36)______________________________ 2010 </p><p> 4 . . 1) . . * 2) . . 3) . . 4) . . 5 3 9 </p><p> 1) </p><p>931 </p><p> * 2) 9</p><p>32 </p><p> 3) 3</p><p>91 </p><p> 4) 3</p><p>92 </p><p> 6 15 10 25 </p><p> 1) 101 * 2) 5</p><p>1 3) 103 4) 2</p><p>1 </p><p> 7 0, 1, 2 3 </p><p> * 1) 4</p><p>1 2) 43 3) 2</p><p>1 4) 32 </p></li><li><p> 2010 ______________________________ (37) </p><p> 8 12 1, 2, ... , 12 4 1 </p><p> 1) 2</p><p>121 </p><p> * 2) 12</p><p>41 </p><p> 3) 12</p><p>21 </p><p> 4) 4</p><p>121 </p><p> 9 A = {1, 2, 3} B = {5, 6, ... , 14} r = {(m, n) | m A n B} 1 r (m, n) 5 </p><p>n 3 1) 15</p><p>1 2) 101 * 3) 5</p><p>1 4) 53 </p><p> 10 1 9 4, 5, 6, 7, 8, 9, 10, 11 </p><p>12 3...</p></li></ul>