
#1
Feb1007, 07:03 PM

P: 460

Given set A and B, the union is defined as
[tex]A\cup B := \{x  x \; \epsilon A \lor x \; \epsilon \; B \}[/tex] But how is [tex]\lor[/tex] defined? 



#2
Feb1007, 07:10 PM

P: 461

It's defined as or. As in A v B is the condition that A holds, or B holds, or both hold.




#3
Feb1007, 07:55 PM

P: 460

But isn't that circular definition? You are defining A OR B as true when either A is true OR B is true OR both are true!




#4
Feb1007, 07:59 PM

HW Helper
P: 1,373

Unions and Intersections
Perhaps this is better. It is a binary function that maps 2tuples of truth values to a truth value which is false for (0,0) and true otherwise.
Oh, perhaps this is circular. 



#5
Feb1007, 08:39 PM

HW Helper
P: 3,225

A  B  A V B
 T  T  T T  F  T F  T  T F  F  F 



#6
Feb1007, 08:50 PM

P: 460

Correct me if I am wrong. You define OR as a function [tex]f: (x,y) \to z[/tex] where [tex] x,y,z \; \epsilon \; \{0, 1\}[/tex] satisfying the following property: [tex](x,y) = (0,0) \Rightarrow z = 0 \land (x,y) \neq (0,0) \Rightarrow z = 1 [/tex] I guess the circularity of this definition depends on how you define [tex]\land[/tex] and [tex]\Rightarrow[/tex]... 



#8
Feb1007, 09:02 PM

Mentor
P: 8,287





#9
Feb1007, 09:27 PM

P: 460

Notice that [tex] p \Rightarrow q : = \lnot p \lor q[/tex] 



#10
Feb1007, 09:29 PM

P: 460





#12
Feb1107, 03:02 AM

Sci Advisor
HW Helper
P: 9,398

There is nothing at all 'circular' in any of these definitions. It would have been better written as
(x in A)v(x in B) to avoid confusion (his A and B are not your A and B). What on earth do you think the definition of logical OR is if not what was given? V is just another symbol for logical OR. Do'nt confuse sets with conditions that define the sets: the defining condition for a union of two sets is the disjunction (OR) of the individual conditions. 



#13
Feb1107, 03:06 PM

P: 461

How on earth is my definition is circular. I said that v is defined to be or. Not that or is defined to be or. Pay attention.




#14
Feb1107, 05:48 PM

P: 460

Anyways, say that you do define v to be or. The how do you then define or? 



#15
Feb1107, 05:52 PM

P: 460





#16
Feb1107, 05:59 PM

Sci Advisor
HW Helper
P: 9,398

Look at the (expletive deleted) truth table. That is how OR and DISJUNCTION are defined (they are after all just different names for the same thing).



Register to reply 
Related Discussions  
probability of unions/intersections  Set Theory, Logic, Probability, Statistics  4  
How Bush helped to legalize gay unions in Oregon  General Discussion  1  
Filling in the blanks proof, having some issues! Set Theory Unions/Subsets  Calculus & Beyond Homework  1  
Labor Unions and Capitalism?  Current Events  69  
Functions, intersections, and unions  Introductory Physics Homework  3 