This page contains interesting questions concerning HW#4 that I have received from students in CMPSCI 601, together with my answers. Questions are in black, answers in blue. Most recently answered questions are listed first.
In Question 9.5, we are told to change the false statements into true ones by inserting or deleting a negation sign. This seems too easy!
It is easy if you are thoroughly familiar with the meaning of the quantifiers and other symbols. The purpose of this exercise is to give you practice with such meanings, and with the software -- the real point is that you know which of those statements are true and which are false, and why they are true or false.
For Question 11.39, I am trying to translate sentence 4:
4: "Every small cube is in back of a particular large cube,"
into a first-order sentence. I have rephrased the sentence as
4a: "There exists a large cube x such that every small cube is in back of x".
But the Grade Grinder says that my symbolic translation of this is wrong.
Your rephrasing is correct, but your symbolic
translation (which I'm omitting here) actually says:
4b: "There exists an object x such that for any object
y, if y is a small cube then x is a large cube and y is in back of x."
This doesn't mean exactly the same thing. For example, if there
are no cubes in the world at all, 4a is false
but your 4b is true (as long as at least one other
object exists). If there are no small cubes in the world, in other words,
4a means "there exists a large cube" 4b means just "there exists an object",
because every object satisfies the implication "if y is a small cube, then..."
because y isn't a small cube.
Should I put Dave's name or Kazu's as "instructor" when the Grade Grinder asks me?
Kazu's, so that the Grade Grinder will send the
scores to him at kazu.cs.umass.edu.
Answers to Questions during HW#3 (through 17 Mar 2003)
Answers to Questions during HW#2 (through 3 Mar 2003)
Answers to Questions during HW#1 (through 12 Feb 2003)
Last modified 29 March 2003