Which of the following statements are true? (a) 100 n2 + n³ -n + 2 = O(n?) (b) 5n²-2n2-n+2=0(n³) (c) 5n - 1000n200 - 2n + 2 =0(2") (d) 5n-1000n200_2n+2=0(n200) a. (a) is true, but (b).(c) and (d) are false O b. (a),(b).(c) are true , (d) are false (a) And (d) are false, (b) and (c) are true O d. (a) And (c) are true, (b) and (d) are false e. (a) And (d) are true, (b) and (c) are false
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- Which of the following best characterizes the statements: A) If n is an odd integer, then n2 + 4n + 1 is an even integer B) If n is an integer that is evenly divisible by 3, then (n + 2)2 + 2n is an even integer 1.Only A is true 2.Only B is true 3.Both A and B are true 4.Both A and B are falseChoose ALL correct statements if more than one are correct. Which of the following statements are true as (n gets large or n →∞)? A. n2 * 5n = O(5n) B. n5 * 2n + n2 * 5nn = O(n2 * 5n ) C. log(n5 + 7) +n2 + n = O(n) D. n0.5 + (0.5)n = O(n0.5) E. None of the above is correct.Which of the following statements is not true if f(n) is O(g(n)): a)f(n) grows more c)f(n) and g(n) have the same growth b)g(n) grows more d)All of the statements mentioned here
- Write a program that calculate the values of (X + Y) x (X – Y) where X, Y = 0, 1, 2, …, 9and prints the following table:X|Y 0 1 2 3 4 5 6 7 8 90| 0 -1 -4 -9 -16 -25 -36 -49 -64 -811| 1 0 -3 -8 -15 -24 -35 -48 -63 -802| 4 3 0 -5 -12 -21 -32 -45 -60 -773| 9 8 5 0 -7 -16 -27 -40 -55 -724| 16 15 12 7 0 -9 -20 -33 -48 -655| 25 24 21 16 9 0 -11 -24 -39 -566| 36 35 32 27 20 11 0 -13 -28 -457| 49 48 45 40 33 24 13 0 -15 -328| 64 63 60 55 48 39 28 15 0 -179| 81 80 77 72 65 56 45 32 17 0Which of the following are correct? (a) A≡B|=(A∨B). (b) (A≡B)|=¬A∨B. (c) (A∧B)→C|=(A→C)∨(B→C). (d) (A∨B)∧(¬C∨¬D∨E)|=(A∨B)∧(¬D∨E). (e) (A ≡ B) ∧ (¬A ∨ B) is satisfiable.What would be the output of the following program?Please note that the operation x % 10 (i.e., x modulo 10) is always the same as the rightmost digit of x (e.g., 123 % 10 = 3).
- Let S = {x | x = 3n, n ∈ Z+}. Which of the following expression(s) is/are true?a. 3 ∈ S b. 3 + 6 ∈ S c. ∅ ⊂ S d. S ⊆ S e. 1 ∈ SWhat is the Big-O notation of the following expression? n3 + n2 + n + 5 a. O(3) b. O(n3) c. O(n) d. O(n2)What is the output of the following program segment? n1 = 27n2 = 18rem = 1n3 = 1while rem != 0: rem = n1 % n2 if rem == 0: n3 = n2 else: n1 = n2 n2 = rem print("Value of n3 is ", n3) Value of n3 is 0 Value of n3 is 18 Value of n3 is 9 Value of n3 is 1
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