(I filled in as much as I could)
need to show is T for 3,13,26
Statment of the Base Step:
3 = L*3+H*10 non-negative integers
13 = L*3+H*10 non-negative integers
26 = L*3+H*10 non-negative integers
Statment of the Base Step:
3 = 1*3+0*10
13 = 1*3+1*10
26 = 2*3+2*10
Statement of the inductive step
Proof of the inductive step
Invoke the principle of strong induction
Since the base step and the inductive step are true by the principle of strong induction all amounts of postage __________ can be obtained using 3 and 10 cent stamps
We are given that the postage can be formed by using the stamps of just 3-cent and 10-cent only,
So such amount can be formed by all linear combinations, where x and y are nonnegative integers. So, possible amounts are:
Here, we can notice that the stamps having amount more than or equal to 18 cents can be formed by just 3-cent and 10-cent stamps.
Now, we will prove the result by strong induction: That amount of postage of c cents can be formed by using just 3-cent and 10-cent stamps.
Let P(c) be the statement that, the amount of postage of c cents can be formed by using just 3-cent and 10-cent stamps.
Take c=18, c=19 and c=20
For P(18), we have
Since, 18 cents can be formed by using six 3-cent So, P(1...
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