Solutions for Sample Exam II

There will be 10 reasonable questions on the exam including the history question. Each question will be half the length and difficulty of those discussed in class.

4. Since the product of the growth rates is the growth rate of the product, it follows that nlogn grows faster than n (since logn grows faster than 1). We say that n is big O(nlogn).

5. {a,{a}}

6. Show that ~(AUB) subset (~A int ~B) x el ~(AUB) implies ~(x el AUB) implies ~ (x el A v x el B) implies x el ~A and x el ~ B implies x el ~A int ~B implies x el (~A int ~B) We leave (~A int ~B) subset ~(AUB) to you.

7. Let U be the array of integers from 1 to 10. Indicate that subsets of U contain elements from U if there is a one in position i of a string while a 0 in position i of the string indicates the element is not present. Thus U= 11 11 11 11 11 11 while A= 10 10 10 10 10.

8. Solve for x as a function of y x g(y)=(y-5)/3 The domain and range are all reals. The verification and plot are left to you.

9. The domain is x>-1 the range is y>0 (one way to find it is to compute the inverse function and find its domain.)

10. 2*2*2*...*2 (nfactors) < 1*2*3*...*n, if n>=4 Since 24>16 and every factor in the later is greater than every factor in the former. Later we will prove this formally by induction.

• About this document ...