home—info—lectures—hws—exams
hw01
hw01
Due 2007.Aug.27
Although you are welcome to typeset your work nicely (using Microsoft Word
or LaTeX or whatever to get nice logic symbols),
it's probably much easier to write formulas by hand.
-
TeachLogic exercises I: #4 (hidden premises in a real-world argument)
- Rosen 1.1, p.16 #10:
Let p, q, and r be the propositions
-
p: You get an A on the final exam
-
q: You do every exercise in this book
-
r: you get an A in this class
Write theses propositions using p, q, and r
and logical connectives.
-
You get an A in this class, but you do not do every exercise in this book
-
You get an A on the final, you do every exercise in this book, and you get an A in this class
-
To get an A in this class it is necessary for you to get an A on the final.
-
You get an A on the final, but you don’t do every exercise in this book; nevertheless, you get an A in this class.
-
Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.
-
You will get an A in this class if and only if you either do every exercise in this book or you get an A on the final.
-
TeachLogic exercises I:
#6 (english → propositional logic)
-
TeachLogic exercises I:
#8 (weasel words)
-
Rosen 1.1, p.18, #24d,e,f:
Construct a truth table for of these compound propositions.
-
(p ∧ q) → (p ∨ q)
-
(q → p) ↔ (p ↔ q)
-
(p ↔q) ⊕ (p ↔ q)
(where “⊕” stands for exclusive-or
(“xor”)
— one or the other but not both)
Which of these — if any — are tautologies?
-
Rosen p.28 #18 (5ed: p.26 #12):
Show that
(p → q)
and
(¬q → ¬p)
are logically equivalent.
-
TeachLogic exercises I:
#17 (equivalences via truth-tables)
Let φ =
(
(a∨c)
∧
(b→c)
∧
(c→a)
),
ψ =
(
(b→c)
∧
a
), and
ω =
(
(a∨c)
∧
(b→c)
).
If you see a few other problems in Rosen which catch your eye,
and you'd like to do them for extra credit, you are welcome to
(though you can ask me for how much; extra-credit is harder to earn
point-per-point than regular credit).
home—info—lectures—hws—exams
rad�ford.edu