## Question-72

Question-72 Prove that if A1 , A2 , …. , An and B1 , B2 … Bn are sets such that Aj Bj for j = 1, 2 ,…, n,…

## Question-71

Question-71 Use mathematical induction to prove that 3 divides + 2 n whenever n is a positive integer.   solution   The statement is true for the base case, n…

## Question-70

Question-70 Prove that 3n < n! if n is an integer greater than 6. The basis step is n = ?. The basis step is true since ?  <  ?…

## Question-69

Question-69 a) Find a formula for  By examining the values of this expression for small values of n. The formula for the sum is ?   b)  Prove the formula…

## Question-68

Question-68 Let P(n) be the statement that 13  + 23  + …. + n3 = for the positive integer n. a)     What is the statement P(1) ? P(1) is the…

## Question-67

Question-67 What is the largest n for which one can solve within one second using an algorithm that requires f(n) bit operations, where each bit operation is carried out in…

## Question-66

Question-66 How much time dose an algorithm take to solve a problem of size n if this algorithm uses operations, each requiring second, with the following values of n ?…

## Question-65

Question-65 What is the largest n for which one can solve within one second a problem using an algorithm that requires f (n) bit operations, where each bit operations, where…

## Question-64

Question-64  There is a more efficient algorithm (in terms of the number of multiplications and additions used) for evaluating polynomials than the conventional algorithm. It is called Horner’s method. This…

## Question-63

Question-63 Give a  big-O estimate for the number of comparisons used by the algorithm that determines the number of 1 s in a bit string n by examining each bit…