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1. Use mathematical induction to prove
whenever n is a positive integer.
2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
INPUT: Integer n
OUTPUT: The sum of 1,...,n
S(n)
1. i ← 0
2. while n>0
3. do i ← i + n
4. n ← n-1
5. return(i)
Proof for Properties of Dot Product Proof of u → • (v → + w → ) = u → • v → + u → • w → We'll begin with the three vectors, u → = (u 1 , u 2 , ...
Write down the system of differential equations for the population of both predators and prey by using the assumptions above. Solution We will start off through letting that
a question
1. Consider the relation on A = {1, 2, 3, 4} with relation matrix: Assume that the rows and columns of the matrix refer to the elements of A in the order 1, 2, 3, 4. (a)
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