27. Show the correctness of the following statements. (a) lg n E O (n) (b) n E O (n lg n) (c) п 1g nE O(n?) (d) 2" E Q sln n (е) Ig3 n € (n95)
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please solve Only C and E
Use L'Hôpital's rule for both
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- Let A={8,9,10}, B={9,10,11,12,15} and C={9,10}. Which of the following statements are true? a) d) {2,5} ⊆ A e) φ ⊆ CState the order of evaluation of the operators in each of the following C statements andshow the value of x after each statement is performed.a) x = 7 + 3 * 6 / 2 - 1;b) x = 2 % 2 + 2 * 2 - 2 / 2;c) x = ( 3 * 9 * ( 3 + ( 9 * 3 / ( 3 ) ) ) );If int x = 10;, int y = 7;, double z = 4.5;, and double w = 2.5;, evaluate each of the following statements, if possible. If it is not possible, state the reason. (3, 4) (x + y) % x x % y + w (z - y) / w (y + z) % x (x % y) * z x % y % 2 (x + y) % z (x % y + z) / w
- 3 5. Say for each of the following sets of statements if they are consistent or inconsistent. A.G Ↄ H / H Ↄ J / J Ↄ K/ K Ↄ ~G b. P ≡ Q / Q v P / P Ↄ X / Q Ↄ ~P c. Z Ↄ [(P ● R) v (L ● P)] / ~P Ↄ ~Z / L Ↄ~ RLet A={8,9,10}, B={9,10,11,12,15} and C={9,10}. Which of the following statements are true? a) 5 ⊆ A b) C ⊆ B c) φ ∈ A1. Write C++ expressions that are equivalent to the following mathematical formula. Assuminga, b, c, e, m1, m2, p, r, and x are separate variables. (a) b^2 + 4ac (b) ? b/c (c) 1/1+√1−? (d) 4/3??2 (e) G = 4π^2 ??^3/?(?1+?2)
- Write C++ statements that accomplish the following. (6, 7)a. Declare int variables x and y. Initialize x to 25 and y to 18.b. Declare and initialize an int variable temp to 10 and a char variable ch to 'A'.c. Update the value of an int variable x by adding 5 to it.d. Declare and initialize a double variable payRate to 12.50.e. Copy the value of an int variable firstNum into an int variable temp Num.f. Swap the contents of the int variables x and y. (Declare additional variables, if necessary.)g. Suppose x and y are double variables. Output the contents of x, y, and the expression x + 12 / y - 18.h. Declare a char variable grade and set the value of grade to 'A'.i. Declare int variables to store four integers.j. Copy the value of a double variable z to the nearest integer into an int variable x.If, A = {3, 5, 7, 9} B = {2, 4, 6, 8, 10} C = {12, 14, 18, 20, 24} D = {21, 26, 31, 36} A. State whether TRUE or False: 1. 13 ∈ C 2. 6 ∉ A 3. 31 ∈ D 4. 20 ∉ B B. Fill in the blanks to make each statement true: 5.) 3 ∈ ___ 6.) 4 ___ B 7.) 26 ___ C 8.) 8 ∈ ___Let a, b, c be integer variables having values 2, 4, 5 respectively and x, y, z be float variables having values 1.1, 2.5, 3.6 respectively. Determine the value of each arithmetic statements. a + b + c a % b a / b a * (b / c) x + y + z x / (y + z) x % y Test B. Copy and answer the following:Interpret and determine the value of each statement. Let integer x = 2, y=5, z = 10 (x<y)&&(y>=z)||(z==x) (y>=x) || !(z==10) && (x<z&&y==2||z>=y) (z%y==x)&&( (y + z)/3>=x)
- Write a single C statement or line that accomplishes each of the following:b) Assign the product of variables b and c to variable aExercise 5-8 Determine which of the following can, and which cannot be added to our set of valid argument forms. (1) p ∨ (q ∨ r) :: r ∨ (q ∨ p) (3) p ⊃ (q ⊃ r) :: r ⊃ (q ⊃ p) (5) p ⊃ q /∴ ∼ (∼ q ⊃ p)2. Assume x, y and z are integer variables with x = 2, y = 5 and z = 10. Each expressionis independent. Determine the results of the following statements and show the step toevaluate them:
