Question

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) {3,4} ⊂ A ???????

Answer 1

yes

{{3,4}} ⊂ A

set A has a subset that has two elements 3 and 4.

Answer 2

It is a little weird, but 3 is not an element of A (nor is 4), but the set {3,4} is an element of A.

Answer 3

visualize it as hierarchy of elements. A has a subset. that subset has elements "3, 4"

Answer 4

ohh, so if there are two braces it means that it is as a whole, the element of A?

Answer 5

yup.. that WHOLE is an element of A

Answer 6

A has four elements. Three of them are the numbers 1,2,and 5. The fourth element of A is the set {3,4}. If we say B = {3,4}, then we can say B is an element of A or B is a subset of A or {{3,4}} is a subset of A or {2,{3,4}} is a subset of A.

Answer 7

A has 4 elements

a 1
a 2
a set containg the numbers 3 and 4

and a 5

Answer 8

@Valpey but in my textbook it is given that {3,4} ⊂ A is incorrect.

Answer 9

your book is correct

Answer 10

\[3\in\{3,4\}\]

but \[3\notin A\]

Answer 11

why please clarify...

Answer 12

thus they can't be subsets

Answer 13

I listed above the 4 elements of A. is any of them just a 3

Answer 14

okay and there is an another question
1 ⊂ A is incorrect?

Answer 15

@Zarkon help me out

Answer 16

{{3,4}} is a subset of A but {3,4} is not a subset of A.

Answer 17

Similarly, 1 is not a subset of A but {1} is a subset of A. 1 is an element of A.

Answer 18

I was wrong to say B was a subset of A. B is just an element of A.

Answer 19

{B} is a subset of A. (where I define B = {3,4} as before)