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 (r ∧ ¬q) You get an A on the final, you do every exercise in this book, and you get an A in this class (p ∧ q ∧ r) To get an A in this class it is necessary for you to get an A on the final. (r → p) 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. (p ∧ ¬q ∧ r) Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class. ((p ∧ q) → r) 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. (r ↔ (p ∨ q)) TeachLogic exercises I: #6 (english → propositional logic) AW → PF (¬PF ∨ BF), which is equivalent to (PF →BF) If we don't use the exclusive-or operator, we can still write this as (AW ∧ ¬ BF) ∨ (¬AQ ∧ BF) TeachLogic exercises I: #8 (weasel words)

Let φ = (weasel → (words ∨ eyed)).
Let φ = (mongoose → ¬weasel).
Let φ = logiconia.
In order for a page to be logiconian, we all these conditions must hold: (φ ∧ φ ∧ φ)

A Logiconian page which doesn't contain weasel might contain mongoose or might not.

This page is not Logiconian, since it contains both mongoose and weasel.

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? (make-truth-table `{"p" "q"} `{[(span {@} "(p" and "q)" rarr "(p" or "q)") ,(lambda (p q) (if (and p q) (or p q) true))] [(span {@} "(q" rarr "p)" harr "(p" harr "q)") ,(lambda (p q) (eq? (if q p true) (eq? p q )))] [(span {@} "(q" harr "p)" oplus "(p" harr "q)") ,(lambda (p q) (xor (eq? q p ) (eq? p q)))] })
Rosen p.28 #18 (5ed: p.26 #12): Show that (p → q) and (¬q → ¬p) are logically equivalent. Make a truth-table for these two formulas, and verify that the column for each formula is the same. 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) ). (listlist->rows '(("a" "b" "c" phi psi omega "note") (false false false false false false "") (false false true false false true "psi,omega differ") (false true false false false false "") (false true true false false true "psi,omega differ") (true false false true true true "") (true false true true true true "") (true true false false false false "") (true true true true true true "")))

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).