## Question

(a)

i=0

j=0

while ( j < 10000):

#LI : 2 * i == j

i = i+2

j = j+4

(b)

i=4

j=2

while ( j < 10000):

#LI : 2 * i == j

i = i+2

j = j+4

(c)

k=0

i=0

while (k <= 10000):

#LI : i == k

k = k + 1

i = i + 2

(d)

n = . . . some positive number . . .

i=0

while ( i < n ) :

# LI : i <= n

i = i + 2

(e)

n = . . . some positive number . . .

i=0

while ( i < n ) :

# LI : i <= n

i = i + 1

## Solution Preview

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Problem 1 (Preserving Invariants)a) The loop invariant is true every iteration of the loop.

i will have values 0, 2, 4, 6, 8, 10, …

j will have values 0, 4, 8, 12, 16, 20, …

It is always true that j is equal to 2 * i

b) The loop invariant is false from the start.

i will have values 4, 6, 8, 10, 12, 14, …...

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