Section answers, 4 April 2011
Julian Jonker
1
How much do you know?
1.
(Ex 9.25) Assume you are working in an extension of the ﬁrstorder language of arithmetic with the
additional predicates
Even(x)
and
Prime(x)
. Express the following in this language, explicitly using
the function symbol
×
, as in
z
×
z
, rather than
z
2
. Note that you do not have predicate
Square(x)
or
Odd(x)
.
(a)
No square is prime.
¬∃
x Prime(x
×
x)
(b)
Some square is odd.
∃
x
¬
Even(x
×
x)
(c)
The square of any prime is prime.
∀
x(Prime(x)
→
Prime(x
×
x))
(d)
The square of any prime other than 2 is odd.
∀
x(Prime(x)
∧
x
>
2
)
→ ¬
Even(x
×
x))
(e)
The square of any number greater than 1 is greater than the number itself.
∀
x(x
>
1
→
x
×
x
>
x)
2. Assess whether the following arguments are (a) tautologically valid, (b) logically valid but not tautologically
valid, or (c) invalid.
(a)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 FITELSON
 Logic, large cube, Z×Z, Julian Jonker

Click to edit the document details