1. ## Logical Formulae

Hey,

I can't do a question and need help ugently, i have been asked to write;

"The Set A has at most 2 elements"

as a Logical Formulae. But have no idea how to go about it.

Thanks

D

2. Originally Posted by dagreenhill
Hey,

I can't do a question and need help ugently, i have been asked to write;

"The Set A has at most 2 elements"

as a Logical Formulae. But have no idea how to go about it.

Thanks

D

$
a, b,c \in A \Rightarrow (a=b) \vee (a=c) \vee (b=c)
$

3. ## blah

Originally Posted by CaptainBlack
$
a, b,c \in A \Rightarrow (a=b) \vee (a=c) \vee (b=c)
$
Thanks!
but..

Is There a less specific way of writing that? A general formula or something? maybe containing "for all"? Or mentioning the empty set? since it is "at most"

4. Originally Posted by dagreenhill
Thanks!
but..

Is There a less specific way of writing that? A general formula or something? maybe containing "for all"? Or mentioning the empty set? since it is "at most"
Since you ask for a formula involving quantification, this is how I'd write it and how you would probably see it written
in most any textbook on axiomatic set theory. As you can see, there's no need for explicit mention of the empty set.
The key here is to recognize that it's a hypothetical statement.

(Note: 'e' denotes set membership; the other symbols should be obvious).

(x)(y)(z) [[(xeA ^ yeA) ^ ~(x = y)] -> [zeA -> [(z = x) V (z = y)]]]

5. Originally Posted by CaptainBlack
$
a, b,c \in A \Rightarrow (a=b) \vee (a=c) \vee (b=c)
$
$(a,b,c) \in A \times A \times A \Rightarrow (a=b) \vee (a=c) \vee (b=c)$

RonL