12
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
Formalize each of the following statements as a boolean expression. Start by staying as
close as possible to the English, then simplify as much as possible (sometimes no
simplification is possible). You w
16
(a)
(b)
(tennis) An advertisement for a tennis magazine says If I'm not playing tennis, I'm
watching tennis. And if I'm not watching tennis, I'm reading about tennis. Assuming the
speaker cannot do more than one of these activities at a time,
prove tha
44
(a)
(b)
(c)
(von Neumann numbers)
Is there any harm in adding the axioms
0 = cfw_null
the empty set
n+1 = cfw_n, ~n
for each natural n
John von Neumann used these axioms as part of his demonstration that set theory could be
used to construct all of mat
55
(a)
(b)
(c)
In each of the following, replace p by
x: int y: int z: int x0 x2y z: int z2y zx
and simplify, assuming x, y, z, u, w: int .
p (x+y) (2u + w) z
x: int y: int z: int x0 x2y z: i
0
There are four cards on a table showing symbols D, E, 2, and 3 (one per card). Each card
has a letter on one side and a digit on the other. Which card(s) do you need to turn over to
determine whether every card with a D on one side has a 3 on the other?
2
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
Prove each of the following laws of Boolean Theory using the proof format given in
Subsection 1.0.1, and any laws listed in Section 11.4. Do not use the Completion Rule.
ab ab
ab
specialization
a
generalization
ab