Question

More Questions...
Problems with Set Theory --Subset-- If every element of a set B is also a member of a set A, then we say B is a subset of A. We use the symbol ⊂ to mean “is a subset of” and the symbol ⊄ to mean “is not a subset of”. But there is a question in my textbook-----let A= {1,2, {3,4},5}. then which of the following statement are incorrect. (i) 1 ∈ A ii. ϕ ∈ A iii.{ϕ } ∈ A

Answer 1

3rd

Answer 2

@ganeshie8 incorrect are 1st and 2nd

Answer 3

sorry are 2nd and 3rd

Answer 4

i think 2nd and 3rd are incorrect

1st is true. A has the element 1 right

Answer 5

yes, it is true but why 2nd and 3rd are incorrect
/

Answer 6

becos there is no "element" ϕ

Answer 7

ϕ ∈ A <------ this statement doesnt say "ϕ" is subset to A. it says the element "ϕ" belongs to A. which is incorrect

Answer 8

okay you mean phi isn't an element. so what it is? every set contains a phi

Answer 9

nope. every set doesnt contain the "element" phi

every set contains an "empty set" phi

Answer 10

ϕ ⊂ A
{} ⊂ A

both above statements are same. empty set is represented using those symbols.

Answer 11

okay i got it

Answer 12

glad to hear ^_^

Answer 13

but this is right ϕ ∈ A ?

Answer 14

no sorry i just was a bit confused..

Answer 15

np :)

thats not right becos it says the element ϕ belongs to A.

we defined ϕ as a "subset" to every set.
we didnt define ϕ as a "element" which belongs to every set.

Answer 16

@ganeshie8 but in my textbook it is given that ϕ ⊂ A it is right. but why?

Answer 17

thats right

ϕ ⊂ A <---- says ϕ is a "subset" to every set

Answer 18

ϕ ∈ A <----- says ϕ is an "element" in every set

Answer 19

first one is true. second is false

Answer 20

"an empty set exists in every set "
"an element ϕ doesnt exist in every set"

Answer 21

oh ganesh that you very much. greeting from india!

Answer 22

yw.. :))