Question

why the elements of AUB just belong to at least one of the sets, I mean if AUB is the sum of the elements of A & B then it means that AUB contains all the elements from A & B so AUB contains all the elements from both A & B, isn't?

Answer 1

@amistre64 if you are free then please help me in understanding the concept of AUB

Answer 2

yes, your argument is valid. Let's take one element, say x in A and B. Thus, x in A and therefore, x is also in AUB.

Answer 3

if you have 1 cent; you have at least 1 cent right?

if you have 4 cents, then you still have at least 1 cent right?

if you have 123 cents, you still have "at least" 1 cent.


the element x has to be a member of "at least" one of the sets

Answer 4

idk

Answer 5

spose A = {a,b,c,d}
B = {a,b,7}

the elements of AuB have to be a member of "at least" A or B

Answer 6

@amistre64 in this case AUB={a,b,c,d,7} and all the elements are neither in A nor in B

Answer 7

so some of the elements are either in A or in B

Answer 8

in the text it says "AUB is meant the set consisting of all elements which belong to at least one of the sets A and B

Answer 9

thats what i said ....

Answer 10

you said some of the elements & the text says all of the elements

Answer 11

what is the set of things in your left pocket?

Answer 12

my syntax is prolly not accurate

Answer 13

tissue paper

Answer 14

and what is the set of all the things in your right pocket?

Answer 15

eraser

Answer 16

ok, then the set of left U right is; all the things that you have in your pockets. the element "paper clip" is not in the set since it is not an element of either set

Answer 17

lol no fence but eraser lol

Answer 18

to be in the set AuB; you have to be at least a member of one of the sets

Answer 19

OK so could it also mean that the U could be a set of the elements of more than one set?

Answer 20

of course; if you are a member of the set A, and a member of the set B; then you are "at least" in one of the sets

Answer 21

& I guess this condition of "at least one set" implies when we take a union of lets say A=(a,b,c} & B={ } isn't?

Answer 22

the union of your defined sets there; AuB = {a,b,c}

Answer 23

the null set is an element of any set regardless

Answer 24

or at least a subset :)

Answer 25

so in this case the elements of AUB just belong to A & not to B whereas the elements of B belong to A as empty set is a subset of every set

Answer 26

is the element "d" a member of either A or B ??

Answer 27

I am considering A={a,b,c} & B={ }

Answer 28

i know, and in order to be an element of AuB; you have to be a member of "at least" one of the sets. therefore, is "d" a member in AuB ?

Answer 29

no

Answer 30

then the definition that you are asking about, holds true

Answer 31

it is not discussing the elements that are in the sets, perse; but it says that in order to be in the union, you have to be at least in one of the sets

Answer 32

how did you relate this d with the definition?

Answer 33

"by AUB is meant
the set consisting of
all elements which belong
to at least one of the sets
A and B"

therefore, in order to be in the set AuB; you have to be a member of at least A or a member of B.

Answer 34

ok &?

Answer 35

if you are NOT at least a member of A or a member of B, then you are NOT in the set AuB

Answer 36

OKKKKKKKKKKKKK

Answer 37

now it's crystal clear

Answer 38

thanks a tonne @amistre64 you are the best

Answer 39

youre welocme