80-110   The Nature of Mathematical Reasoning

Spring 2001

Dirk Schlimm

Homework No.8

Thursday, March 15, 2001
Due Tuesday, March 20, 2001

1. Probability theory (4 points)

a) Prove Bayes' Theorem: P(H|E)=[ P(E|H)*P(H) ] / P(E)
from the axioms and definitions introduced in class.

b) Assume that H stands for "The hypothesis is true" and E stands for "There is evidence that supports the hypothesis". Under this interpretation, what does P(E|H) mean? What probabilities do you need to know, in order to determine the value for the probability that the hypothesis is true given that there is evidence for it?

2. Syllogisms (3 points)

Read Handout #20. Do the following problems:

3. The Language of First-Order Logic (3 points)

In FOL read,

Do the problems listed below. Hand in your answers on a disk (in PC/IBM format). Name your files 3-6.WLD, 3-7-1.WLD, and 3-7-2.WLD