Question

How do you read the symmetric difference between set A and B?

Answer 1

like you would read
\[5 \in B\]
as 5 is a member of set B,

How would you read the proper way?

Answer 2

Need more information, like what are A, B?

Answer 3

A and B are subsets of the universal set. The intersection of A and B is not an empty set.

Isn't there a simple way to read it...the thing is each time I come across this I want to be able to read it like all the other symbols, instead of just thinking 'new cross symbol, whose-name-I-don't-know'

Answer 4

the symmetric difference you can think of as the exclusive or

Answer 5

but shouldn't ewe call it something else, because you call it an exclusive or in compound statements, when your putting two or more propositions together.

Answer 6

$$\Large {
x \in A \oplus B \\\
\iff \\x \in (A \cup B) \smallsetminus (A \cap B )
\\ \iff \\
x \in (A \cup B) ~\land ~x\notin (A \cap B )

}$$

Answer 7

sorry i dont understand your question

Answer 8

the symmetric difference is a type of set operator, that given two sets makes a new set, either-or but not both

Answer 9

ok, I get it....so can I read it as A and B but not both?

Answer 10

x is in A or B, but not both in A and B

Answer 11

thank you, you know that your the only one that gave a proper answer. Some random person even gave me a medal for asking the question...like "Say what?"

Answer 12

your welcome :)

Answer 13

theres a nice picture of the symmetric difference using venn diagrams on the top of this
article .
http://en.wikipedia.org/wiki/Symmetric_difference

Answer 14

hey, check this out, the symmetric difference and the exclusive or have just that one symbol in common
http://en.wikipedia.org/wiki/Exclusive_or

Answer 15

i should have been more careful with my language. strictly speaking `exclusive or` deals with two propositions , while `symmetric difference` deals with two sets (two classes).
They do have similarity, but sets and propositions are different things.

Answer 16

$$

\Large{ A \triangle B\\

p \oplus q }

$$

Answer 17

yeah
```
I figured it out,
I figured it out from black and white
Seconds and hours,
Maybe (I) had to take some time
```
LOL,
yeah got it

Answer 18

for symmetric difference is best to use triangle, but some books use the circle plus too

Answer 19

yeah my book uses the circle and plus exclusively

Answer 20

you can usually tell by context whether you are talking about sets or propositions. we use upper case letters A,B,C for sets, lower case letters p,q, r, for propositions

Answer 21

oh ok :)

Answer 22

I was just feelin lame, ignore me, I heard it in a shop, the bands name has something to do with a single direction or something

Answer 23

but the term 'exclusive-or' refers to propositions, not sets.
the term 'symmetric difference' refers to sets, not propositions.
but the symbol they use may overlap

Answer 24

I had to look that word up...but I appreciate it =)

Answer 25

Generally speaking , in math its bad when you use the same symbol for two different things .
Especially since we can just use a triangle symbol for symmetric difference.
The circle plus is used prevalently in logic and digital design.