Proof of Correctness:
For m (- N, we define predicate Q(m) as follows
Q(m):if k (- N and k >= 1, and m = k, then k_th_even_natural(k) terminates and returns the kth
natural even number.
Want to prove: \-/ m (- N and m >= 1, Q(m) and correctness follows
By PCI: \-/ m (- N and m >= 1, Q(m)
Basis: let m =1. Then k =1
Then k_th_even_natural(k) returns 0 equal to the first even natural number as wanted. (by
Induction Step: Let m >= 2, so k = m >= 2.
Suppose Q(j) holds whenever 0 <= j <= m [IH]
For k >= 2, k_th_even_natural(k) executes line 4
Since 1 <= k-1 < k (by IH)
k_th_even_natural(k-1) terminates and returns the (k-1)th even natural number.
Therefore by line 4, k_th_even_natural(k) returns (k-1)th even natural number +
2 as wanted. EESA09 Participation#1 - Wind Analysis Map
a) Write down the cities that you are comparing for the participation, and the date and the exact time of
The two cities that I compared are Regina and Halifax at 8:00am Toronto time on June 20,2013. Since
Toronto is 2 hours behind Regina and 1 hour ahead of Halifax, at 8:00am Toronto time, Regina is 6:00am
and Halifax is 9:00am on June 20,2013.
b) Record the wind speed and the direction in these cities for the exact time of the day you are working on
the assignment, which describes the current condition.
Current Condition for Regina at 6:00am(8:00am in Toronto): The wind is travelling at 41 km/h and, it is
coming from West and is blowing towards the East.
Current Condition for Halifax at 9:00am(8:00am in Toronto): The wind is trav