Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

My task is consider the set

V = {b, d, f , g, {f , g}, {d, e, f} , {{d}, e} }

R = {c, d, e, f , g}

S = {f , g}

T = {d}

Classify each of the following statements as true or false.

(1) a ∈ V
(2) b ∈ V
(3) c ∉ V
(4) d ∉ V
(5) R ⊆ V
(6) S ⊆ V
(7) S ∈ V
(8) T ∈ V
(9) {d, e, f} ⊆ V
(10) {d, e, f} ∈ V
(11) {{d, e, f}} ⊆ V
(12) {{d, e, f}} ∈ V
(13) {T} ⊆ V
(14) {{T}} ⊆ V

My answers are

1)  False
2)  True
3)  True
4)  False
5)  False
6)  False
7)  True
8)  False
9)  False
10) True
11) True
12) False
13) False
14) True

I`m especially concerned about the last three statements in which i am not really sure.

share|cite|improve this question
(12)-(13) I agree with you, but about (14): it is true iff $\;\{T\}\in V\;$ this last statement true? Since $\;T=\{d\}\;$, we have that $\;\{T\}=\{\{d\}\}\;$. Is this last an element of $\;V\;$ – DonAntonio Apr 19 '14 at 15:25

The only things that I could find is

  • 6 is true

  • 14 is false

For 6: The question is: Is $\{f,g \}\subset V$. This is true exactly when $f,g\in V$. This is true.

For 14: The questions is: Is $\{\{\{d\}\}\} \subset V$. This is true exactly when $\{\{d\}\} \in V$ and this is false.

share|cite|improve this answer
Would it be right to say for 6 that {f,g} ∈ V but {f,g} ⊈ V? – user3077612 Apr 19 '14 at 15:56
@user144257: Both of $\{f,g\}\in V$ and $\{f,g\}\subseteq V$ are true, but for different (and unrelated) reasons. $\{f,g\}\in V$ because $\{f,g\}$ is an element of $V$. And $\{f,g\}\subseteq V$ because $f$ is an element of $V$ and $g$ is an element of $V$. – Henning Makholm Apr 19 '14 at 16:02

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.