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.
Rosen 6ed: p47, #10
(= Rosen 5ed: p40, #10):
(raining cats and dogs ... and ferrets.)
∃s.(C(s)∧D(s)∧F(s))∀s.(C(s)∨D(s)∨F(s))∃s.(C(s)∧¬D(s)∧F(s))¬∃s.(C(s)∧D(s)∧F(s))(∃s.C(s))∧(∃t.D(t))∧(∃v.F(v)).
Note that there are several equivalent ways of saying this:
(∃s.C(s))∧(∃s.D(s))∧(∃s.F(s)) is certainly fine,
and we can also move all the quantifiers out front:
(∃s∃t∃v.(C(s)∧D(t)∧F(v)).
Note that all phrasings, if a single student owns all three types of
animals, then the formula is still true.
Rosen 6ed: p61, #33
(= Rosen 5ed: p55, #33):
Pushing negation over quantifiers, (a)-(e).
See back of book
TeachLogic exercises III: #11
(an even prime?)
y=2 makes the statement true:
P(y)∧(y>2) is false, and F&rarrow;T is true.
Note that y=1 also witnesses the ∃ as being true.
Yes; again, y=2 or y=1 both make the formula true.
No -- an existential formula is false on the empty domain
(even ∃x.(x=x),
or more degenerately ∃x.true).
There exists an even prime greater than 2
would be written as
∃y.(P(y)∧(y>2)∧E(y)).
This statement is false, under the standard interpretation.
TeachLogic exercises III: #12
(interpretations)
Extra Credit:
TeachLogic exercises III: #15
(translating sayings into first-order logic)
Extra Credit:
TeachLogic exercises III: #18
Writing formulas about sequences.
Rosen 6ed: p72, #4
(= Rosen 5ed: p73, #2):
Which rule of inference used in the English arguments about...
Kangaroos in Australia, etc.
Simplification (concluding p from knowing p∧q)
Disjunctive syllogism
modus ponens
addition
hypothetical syllogism
Rosen 6ed: p72, #6
(= Rosen 5ed: p73, #4):
Create an argument about sailing weather.
Like a geometry proof,
each line of your answer is a statement,
plus (on the right) a justification which is
either "premise"
or
one of the rules from Rosen's Table 1.If you prefer
you can use the
Teachlogic inference rules
— pretty much the same rules with clearer names
Rosen 6ed: p73, #10
(= Rosen 5ed: p73, #8):
Find a relevant conclusion, with a justification;
sore hockey etc
premise
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).