Could you help me with these problems please.

1.)Strong induction requires a weaker inductive hypothesis than regular induction.

a)

True

b)

False

2.) Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps. What must be proved to be true in the base case?

a)

P(8)

b)	P(8) and P(9)

c)	P(8), P(9) and P(10)

d)	p(9), p(10) and P(11)

3.) If f(n)= 2f(n1)+6, f(0)=3. f(2) = ?

a)

12

b)

24

c)

30

d)

18

4.)The string of parentheses ()(()))are properly nested?

a)

True

b)

False

5.) Let S be the subset of the set of ordered pairs of integers defined recursively by

Basis step: (0, 0) S.

Recursive step: If (a,b) S, then (a + 2,b + 3) S and(a+3,b+2)S.

Which of the following ordered pairs is an element in S?

a)

(5,5)

b)

(0,3)

c)

(2,0)

d)

(2,2)

6.) Given the recursive algorithm to compute the factorial function as follow:

Input: A non-negative integer n. Output: n!

Factorial(n){ If (n = 0), Return( 1 ) r := Factorial( n - 1 ) // The recursive call Return( r*n )

}

How many multiplication operations are performed in Factorial( 5 )?

a)

6

b)

5

c)

4

d)

7