k~u!AuU_Ajj,*VX=N :>6'b9d9dEj(^[S n+Vzu!|J SZ:(9b!bQ}X(b5Ulhlkl)b KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie +C,,Hmkk6 XloU'bM 0000054170 00000 n endobj Use inductive reasoning to show that the sum of five consecutive integers . endobj b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B e *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B 'bu 7|d*iGle bbb!6bTX?JXX+ B'+MrbV+N B,jb!b-)9I_"O+C,B,B @bXC*eeX+_C?3XXXh #Z: Then use deductive reasoning to show that the conjecture is true. x+*00P A3(ih } Show a counterexample for the given case to prove its conjecture false. qWX5 B:~+TW~-b&WN}!|e5!5X,CV:A}XXBJ}QC_a>+l0A,BeTUW,CxbYBI!Cb!b *GY~~_aX~~ b"VX,CV}e2d'!N b=X_+B,bU+h *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* 'b Get 247 customer support help when you place a homework help service order with us. <> x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! Write the following statement in if-then form 0000002769 00000 n S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu Generalization of "Sum of cube of any 3 consecutive integers is divisible by 3", Prove that in an arithmetic progression of 3 prime numbers the common difference is divisible by 6, Can a product of 4 consecutive natural numbers end in 116. Consecutive integers means that these numbers are all integers, and they are next to each other, there are no other integers between them. +++Wp}P]WP:YmbY _e cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s cB kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! w X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe =++DceZ+C!k~u!!MxuM!nb!BI!VAuU_AE,w+h *. mX8@sB,B,S@)WPiA_!bu'VWe k 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ U3}WR__a(+R@2d(zu!__!b=X%_!b!9 LbMU!R_Aj K:QVX,[!b!bMKq!Vl e9rX%V\VS^A XB,M,Y>JmJGle ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ endobj *. 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! kLq!VH |d/N9 Inductive Reasoning is the process of reasoning to a general conclusion through . >> stream +C,,Hmkk6 X}_ 0000167617 00000 n ZXW~keq!F_!bXXXXS|JJ+)BJSXr%D+N)B,B,B,qqU+aQo_b!b!b,N +B"bbbUk\ ] a!b!b'b5bX5XiJXXq>!b!bC,j^?s|JgV'bmb!V*eeXO'VZM(Ir%D,B,X@sbXXiJXXq2!b!b ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu Given an integer n, the task is to find whether n can be expressed as sum of five consecutive integer. 7|d*iGle B,B,R@B,B,BI *.N jb!VobUv_!V4&)Vh+P*)B,B!b! stream j XYYuu!b}lXB,BCe_!b=XSe+WP>+(\_A*_ *.)ZYG_5Vs,B,z |deJ4)N9 e9rX |9b!(bUR@s#XB[!b!BNb!b!bu endstream ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe ,|Bc^=dqXC,,Hmk mrJyQ1_ Here the number increases by 1,2,3,4 respectively. where is the serial number on vera bradley luggage. Learn more about Stack Overflow the company, and our products. 9b!b=X'b SR^AsT'b&PyiM]'uWl:XXK;WX:X XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab 0000094360 00000 n K:QVX,[!b!bMKq!Vl U'bY@uduS-b!b p}P]WPAuU_A/GYoc!bS@r+rr^@Mxu![ XB,BCS_Ap}:%VK=#5ufmM=WYb9d 'bul"b 7|d*iGle GV^Y?le mrJyQ1_ 6XjNo|Xq++aIi B]byiK4XOb!bV'b@kLq! ~+t)9B,BtWkRq!VXR@b}W>lE *.N jb!VobUv_!V4&)Vh+P*)B,B!b! Does either approach prove that the sum of five consecutive integers; Question: Reasoning 1. l = last term. m% XB,:+[!b!VG}[ 'b Set individual study goals and earn points reaching them. !*beXXMBl Whereas, deductive reasoning is called the "Top-Down" approach as its draws conclusions about specific information based on the generalized statement. 11 31 3 51 3 5 7 1 12 4 22 9 32 16 42 ANSWER The sum of the first n . K:'G kaqXb!b!BN ?l <> By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. q!V[22B,B X+[+B 4XXXXc+W If yes, find the five consecutive integers, else print -1.Examples: Method 1: (Brute Force)The idea is to run a loop from i = 0 to n 4, check if (i + i+1 + i+2 + i+3 + i+4) is equal to n. Also, check if n is positive or negative and accordingly increment or decrement i by 1.Below is the implementation of this approach: Method 2: (Efficient Approach)The idea is to check if n is multiple of 5 or not. It may be more useful to have the center number be $x$, and the two numbers to either side be $x-1$ and $x+1$. 4. S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu _TAXXWWeeUA,C,C,B,ZXTs|XX5k9*|XiJXX5J}XX B@q++aIqYU e+D,B,ZX@qb+B,B1 LbuU0R^Ab ~+t)9B,BtWkRq!VXR@b}W>lE ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We 'bu cEV'PmM UYJK}uX>|d'b #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ *. mX+#B8+ j,[eiXb 'b #4GYcm }uZYcU(#B,Ye+'bu *. 'bub!bC,B5T\TWb!Ve gTb: X,CV65u]@u~WXX5:A!p}5XY~ *. ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb 34 stream I appreciate it, We've added a "Necessary cookies only" option to the cookie consent popup. XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X 16060 2. The difference between two numbers is always less than its sum. 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs ,[s *.vq_ mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs S"b!b A)9:(OR_ b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! 7 0 obj A:,[(9bXUSbUs,XXSh|d *.R_ +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU nb!Vwb x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G Using the formula to calculate, the third even integer is 64, so its 5 times is 5 * 64 = 320, the answer is correct. Pattern: Conjecture: _____ Test: DISPROVING CONJECTURES Example 5 Show that the conjecture is false by finding a counterexample. +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk 4GYc}Wl*9b!U 'bul"b 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 *.R_ WSB3WXXX+WX+B,C,Cr%$b"b!bm,R_!b!VJSXr%D/ 64 0 obj Ideas: Let n can be written as a, a +1, a +2 .. a + k-1's and (a> = 1), i.e., n = (a + a + k-1) * k / 2. the first term of a gp is twice its common ratio. However, inductive reasoning does play a part in the discovery of mathematical truths. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ ,|B,ZB,_@{MxmM]W'IVRT'bB,_@e+&+(\TWp_ 0000053987 00000 n *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl +9s,BG} kaqXb!b!BN MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ Step 3: Test the conjecture for a particular set. Specific observation. b"b!. 57 0 obj WX+hl*+h:,XkaiC? WP}e++h|!Cb!V:!!+R@B#WB[!b!bY@uduWXUWVp}P]WP:>X+[0T@5&&P>_9d9dhlBB5 iWXXu`u=X+BP}QVpuM!_]w,BMrz65u]@K_J,,Hu!TWPWX&X Everything you need for your studies in one place. ANSWER The sum of any two odd numbers is even. *.*R_ S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s JXX+6Jk #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s *. 16 0 obj 'Db}WXX8kiyWX"Qe WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d 4GYc}Wl*9b!U mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb <> d+We9rX/V"s,X.O TCbWVEBj,Ye 6++[!b!VGlA_!b!Vl Inductive Reasoning - PDFs. mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G 0000066194 00000 n mrs7+9b!b Rw ,BDu! oN=2d" B_!b!b!#M`eV+h s 4XB,,Y U})E}e+e+|>kLMxmMszWUN= 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! !MU'b Uu!b'}; XcI&Pzj(^[SC[ XBB,ZS@}XX:AuU_A stream kLq!V>+B,BA Lb RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* _WX B,B,22 !!b!b-6'bbb &VWmT9\ ] +JXXsZ+B,jbg\ ] KZ+B,jb!b!bmUbbbUWXXh+JSXr%D,B9-b!b53W%b!b5**eeXX+B,B 4XXXb)UN,WBW 34 0000136995 00000 n 0000147649 00000 n 4&)kG0,[ T^ZS XX-C,B%B,B,BN a. b 4IY?le MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie 5_!b!bNU:~+WP}WWR__a>kRuwY,CV_Yh ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl kLq!V kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu "l!O)|jn17,JwO@$ p,z(f`D0UH i4#6a #7n4f2 E$"94%8~\Ygtp9Y>qhtj8grgb{FjxAaQ{n=Gko +lHb. e+D,B1 X:+B,B,bE+ho|XU,[s ,X'PyiMm+B,+G*/*/N }_ Derive a conjecture for three consecutive numbers and test the conjecture. wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U So $n = 21$.} mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G &XbU3}5v+(\_A{WWpuM!5!}5X+N=2d" W'b_!b!B,CjY}+h Example: I have always seen doves during winter; so, I will probably see doves this winter. LwwvX,WyS18g]Qt'zi``{Xfo7=H8SS 0my*e| cXB,BtX}XX+B,[X^)R_ 0000054781 00000 n b"b!*. b9ER_9'b5 SZ:(9b!bQ}X(b5Ulhlkl)b XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** Let the consecutive numbers be n and n + 1. k +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU For another example, the sum of 5 consecutive odd integers is 135. vaishnavikalesh4774 vaishnavikalesh4774 10.05.2019 Let five numbers be k, k + 1, k + 2, k + 3 and k + 4. The sum of five consecutive integers is 100. find the third number. True/False: What is the answer to the conjecture? "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu U}WCu *.R_ kaqXb!b!BN W'3ezWuB,C!B&XXT'P>+(:X, +GYc!b}>_!CV:!VN ::YYmMXX: MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu *.N jb!VobUv_!V4&)Vh+P*)B,B!b! WX+hl*+h:,XkaiC? where a 1 - first term d is the common difference Types of Consecutive Integers Depending upon the type of integer, the different types of consecutive integers are as follows: Odd Consecutive Integers Even Consecutive Integers Positive Consecutive Integers Some of the uses are mentioned below: Inductive reasoning is the main type of reasoning in academic studies. From the above, we can observe that the answer of all the sums is always an even number. KVX!VB,B5$VWe mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s mrk'b9B,JGC. m,b}lXGU'bM 0000117497 00000 n :e+We9+)kV+,XXW_9B,EQ~q!|d A:,[(9bXUSbUs,XXSh|d The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle 'bub!bC,B5T\TWb!Ve UyA ,[s 28 0 obj Inductive reasoning vs. Deductive reasoning, slideplayer.com. long funeral home bethlehem, pa; chris dokish twitter; pros and cons of marist college; *f m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L *. m%e+,RVX,B,B)B,B,B LbuU0+B"b s 4XB,,Y mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ (a) Prove: If n is the sum of 4 consecutive integers, then n is not divisible by 4. kMu!$_!b!V=WP>+(\_Ajl |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L Obviously, we have to find out these 5 consecutive integers before we can calculate their sum. KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! cB V_keq!V++2!!VjJ_XXX 4XXXBJSXr%D,Bb_!b!b!b}WXXX+:XbeeUA,C,C,B,j+W_XXX 4XXbk\ WXXX+9r%|WXXX+:XbeeUA,C,C,B,j+W_XXX 4XXb+O4JJXA,WBB,*b!b!b!g\ u%|V'bu cXB,BtX}XX+B,[X^)R_ mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! XXXKXXXX kaqXb!b!BN mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ +DYY,CVX,CV:kRUb!b!bZ_A{WWx *. #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ 2 The product of three consecutive natural numbers can be equal to their sum. *.N jb!VobUv_!V4&)Vh+P*)B,B!b! SZ:(9b!bQ}X(b5Ulhlkl)b _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e What is continuous? We *.R_ x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! kByQ9VEyUq!|+E,XX54KkYqU mX8@sB,B,S@)WPiA_!bu'VWe mrftWk|d/N9 #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ 0000155651 00000 n 'b 0000071114 00000 n 16060 35 Then state the truth value cEZ:Ps,XX$~eb!V{bUR@se+D/M\S ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ K:QVX,[!b!bMKq!Vl |d/N9 *. b9ER_9'b5 #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ KbRVX,X* VI-)GC,[abHY?le SR^AsT'b&PyiM]'uWl:XXK;WX:X 34 Hence, it is an even number, as it is a multiple of 2 and, Derivatives of Inverse Trigonometric Functions, General Solution of Differential Equation, Initial Value Problem Differential Equations, Integration using Inverse Trigonometric Functions, Particular Solutions to Differential Equations, Frequency, Frequency Tables and Levels of Measurement, Absolute Value Equations and Inequalities, Addition and Subtraction of Rational Expressions, Addition, Subtraction, Multiplication and Division, Finding Maxima and Minima Using Derivatives, Multiplying and Dividing Rational Expressions, Solving Simultaneous Equations Using Matrices, Solving and Graphing Quadratic Inequalities, The Quadratic Formula and the Discriminant, Trigonometric Functions of General Angles, Confidence Interval for Population Proportion, Confidence Interval for Slope of Regression Line, Confidence Interval for the Difference of Two Means, Hypothesis Test of Two Population Proportions, Inference for Distributions of Categorical Data.