which of the following are true for the follwing sets?

Question

Let Let A={∅,{∅,{∅}}} B=∅,C={∅},D={∅,{∅}} Which of the following are true,

a). $C\subseteq A\;\;b) \;C\epsilon A\;\; c)\; B\epsilon A\; d)\; B\subseteq A\;e)\;B\epsilon C\;f)\;C=B\;g)\;C\subseteq D\;h)\;C\epsilon D\;i)\;D\subseteq A $

My attempt :a is wright and b is wright confusing about c

b) $C$ is the set containing the empty set, does $A$ also have a set containing the empty set only? — lEm, Mar 19 '16 at 05:11
$C\in A$ means that $C$ is an element of $A$, but as you see, there is no such element (a set containing the empty set only) — lEm, Mar 19 '16 at 05:14
You should spend some time on learning how to write math symbols. This site uses MathJax formatting — JKnecht, Mar 19 '16 at 05:14
These are all sets. The elements of the sets are other sets. B is the empty set and has no elements. C is a set that contains element-- that element is C. So f is false. C and B are different sets. e is true because B, the empty set, is an element of C, the set that contains the empty set. D is a set with two elements. These elements are the empty set, and the set containing the empty set. g is true because every element of C is an element of D. h is true because C itself is an element D. — fleablood, Mar 19 '16 at 05:44
Nearly a duplicate of http://math.stackexchange.com/questions/527819/element-of-subset-of-and-empty-sets/528184#528184 — Michael Hoppe, Mar 19 '16 at 11:20

score 1 · Answer 1 · answered Mar 19 '16 at 05:52

This question is about whats the difference between being an element of a set and being a subset of a set

Consider

$A=\{a,b,c,\{a,b\},\{b,c,d\}\}$

$a$ is an element of the set $A$.

The set $\{a,b\}$ is an element of the set $A$.

The set $\{b,c,d\}$ is an element of the set $A$

The set $\{b,c\}$ is a subset of $A$.

The set $\{a\}$ is a subset of $A$.

$\subseteq$ means subset of

$\in$ means an element of

which of the following are true for the follwing sets?

1 Answers1