What does a set with brackets means?

[inshome]

I need to prove the following whether it is true or not

Let A = [ a, {b, c, d}, {e}, f, {g, h}, {i, j}, k ]
1. {b, c, d} ∈ A
2. {{i, j}} ⊆ A
3. ∅ ∈ A
4. {i, j, k} ∈ A
5. {a} ⊆ A

but I am not sure what does a set with square brackets and curly braces inside it mean. Please help me, thank you!

 

[pka]

I need to prove the following whether it is true or not

Let A = [ a, {b, c, d}, {e}, f, {g, h}, {i, j}, k ]
1. {b, c, d} ∈ A
2. {{i, j}} ⊆ A
3. ∅ ∈ A
4. {i, j, k} ∈ A
5. {a} ⊆ A

but I am not sure what does a set with square brackets and curly braces inside it mean. Please help me, thank you!

Only your textbook, your class notes or your instructor can answer that question.
That is non-standard notation.

 

[ISTER_REG]

For my view brackets in brackets can be translated with a set within a a set. Then I would say for instance that 1. is true (the set/element {b,c,d} is truly an element of the "superset" A) and 2. is also true (The set {{i,j}} is a sub-set of A). Interesting is 3. (for me) the empty set is a sub-set of every set, so I would agree with that statement (even if the empty set is not even listed in the set A...)

But, as pka said, the definition here is not clear...

 

[Dr.Peterson]

I need to prove the following whether it is true or not

Let A = [ a, {b, c, d}, {e}, f, {g, h}, {i, j}, k ]
1. {b, c, d} ∈ A
2. {{i, j}} ⊆ A
3. ∅ ∈ A
4. {i, j, k} ∈ A
5. {a} ⊆ A

but I am not sure what does a set with square brackets and curly braces inside it mean. Please help me, thank you!

The questions all make sense if the brackets are replaced with braces; that is, if the problem were this,

Let A = { a, {b, c, d}, {e}, f, {g, h}, {i, j}, k }​

1. {b, c, d} ∈ A​

2. {{i, j}} ⊆ A​

3. ∅ ∈ A​

4. {i, j, k} ∈ A​

5. {a} ⊆ A​

then part 3 asks whether the empty set is a member (as opposed to a subset) of A, to which the answer is NO.

The brackets could be a typo; or the author might have told you that they (contrary to standard usage) sometimes use [ ] in place of { } just to make it easier to match pairs, as we do with parentheses for [ ( ) ].

It is possible, however, that they use brackets to mean something entirely different, particularly if this is more advanced than a mere introduction to the set concept, as I think it is.

Have you see any other examples or definitions with this notation?

 

[ISTER_REG]

Correction to my post in #3, just because the empty set is a subset of all sets does not mean that it is also explicitly mentioned here in set A... So [MATH]\emptyset \in A[/MATH] is wrong

 

[lex]

1, 3, 4 should be easy - you just look and see if the object is in A
2,5 just look at your definition of subset. Every element of the proposed subset, must be an element of A

The set with square brackets - I don't know. Presumably it should be { }. The curly brackets inside the set just means that some of the elements in the set A are themselves sets.

 

[inshome]

Ok, I think the brackets are just the same with curly braces.

I have another question, is the number 4 false? I am not sure but I think it should be {{8,9},10} to be true

 

[pka]

Ok, I think the brackets are just the same with curly braces.
I have another question, is the number 4 false? I am not sure but I think it should be {{8,9},10} to be true

The set \(A\) contains seven elements. Is the set \(\{i,j,k\}\) one of those elements?

 

[lex]

I am not sure but I think it should be {{8,9},10} to be true

{{8,9},10}? Do you mean {{i,j},k}?

{{i,j},k} is not a member of A.
{i,j} and k are two members.

When you remove the outside brackets from the set A, you are left with a list of the 7 elements of A (with commas in between them):
a, {b, c, d}, {e}, f, {g, h}, {i, j}, k

You get the subsets of A by putting curly brackets around some (or none) of this list of elements, with commas in between.
e.g. [MATH]\boldsymbol{\{}[/MATH] {I, j}, k [MATH]\boldsymbol{\}}[/MATH] is a subset of A
e.g. [MATH]\boldsymbol{\{}[/MATH] a, {e}, k [MATH]\boldsymbol{\}}[/MATH] is a subset of A
e.g. [MATH]\boldsymbol{\{}[/MATH] [MATH]\boldsymbol{\}}[/MATH] is a subset of A

 

[lex]

{ {8,9},10 }? Do you mean { {i,j}, k }?

{ {i,j}, k } is not a member (element) of A.
{i,j} and k are two members of A.

When you remove the outside brackets from the set A, you are left with a list of the 7 elements of A (with commas in between them):
a, {b, c, d}, {e}, f, {g, h}, {i, j}, k

You get the subsets of A by putting curly brackets around some (or none) of this list of elements, with commas in between.
e.g. [MATH]\boldsymbol{\{}[/MATH] {i, j}, k [MATH]\boldsymbol{\}}[/MATH] is a subset of A
e.g. [MATH]\boldsymbol{\{}[/MATH] a, {e}, k [MATH]\boldsymbol{\}}[/MATH] is a subset of A
e.g. [MATH]\boldsymbol{\{}[/MATH] [MATH]\boldsymbol{\}}[/MATH] is a subset of A

 

[inshome]

{{8,9},10}? Do you mean {{i,j},k}?

{{i,j},k} is not a member of A.
{i,j} and k are two members.

When you remove the outside brackets from the set A, you are left with a list of the 7 elements of A (with commas in between them):
a, {b, c, d}, {e}, f, {g, h}, {i, j}, k

You get the subsets of A by putting curly brackets around some (or none) of this list of elements, with commas in between.
e.g. [MATH]\boldsymbol{\{}[/MATH] {I, j}, k [MATH]\boldsymbol{\}}[/MATH] is a subset of A
e.g. [MATH]\boldsymbol{\{}[/MATH] a, {e}, k [MATH]\boldsymbol{\}}[/MATH] is a subset of A
e.g. [MATH]\boldsymbol{\{}[/MATH] [MATH]\boldsymbol{\}}[/MATH] is a subset of A

Thank you very much, I now understand!

 

[lex]

Great. You need to have clear notions of what the elements are and what a subset is, in order to answer these questions. This is a method hopefully you can apply each time you get questions like this.