Apparently nullology is a thing. I think it shouldn't be. (Maybe merge it into elementary-set-theory is a good idea?)

The empty set is a member of $P({a,b}) \times P({p,q})$. True or false? My first instinct was false, since the empty set is a member of each power set individually, but when multiplied together, you get {0,0}, which I'm not sure represents the empty set. But my counter argument is that the empty...

Currently taking a logic class and trying to understand this. You have two set $A$ and $B$. Both sets are empty sets. Is set $A$ a subset of the complement of set $B$? Assume the context is the universal set.

I am working on a problem with the following set: $$S = \{\varnothing,\{\varnothing\}\}$$ My solution was: $P(S) = \{\varnothing, \{\varnothing\},\{ \varnothing , \{ \varnothing \}\}\}$, but the solution on the textbook shows: $P(S) = \{ \varnothing , \{ \varnothing \}, \{\{\varnothing\}\}, \{...

I have some home work with problems such as... Determine whether each of these sets is the power set of a set: {∅, {a}} ∅ So yes 1 is the power set of {a}. But what about 2? Since power sets have to have $2^k$ members then no it can't be a power set. It would have to be P(∅) = {∅, {∅}} corr...

Is $\{\}, \, \{\{\}\},\, \{\{\{\}\}\}$ is an empty set or not? My opinion: the first is the empty set because it contains no elements, while the second and third are not an empty set because it contains a empty set. Please explain to me the given question in detail.

If $A_\alpha$ are subsets of a set $S$ then $\bigcup_{\alpha \in I}A_\alpha$ = "all $x \in S$ so that $x$ is in at least one $A_\alpha$" $\bigcap_{\alpha \in I} A_\alpha$ = "all $x \in S$ so that $x$ is in all $A_\alpha$" It is the convention that $\bigcup_{\alpha \in \emptyset}A_\alpha = \em...

The question arises from the following statements: * " $\varnothing$ is a subset of every set. This fact (that $\varnothing \subseteq A$ for any A) is "vacuously true" (...) " (Enderton - Elements of Set Theory) Okay, so I understand that the empty set is included in every other set. So far ...

I know that by definition, ∅ is a subset of every set but I have a doubt about it appearing as an explicit element of a set. In a union between sets and the finding of the Power of that set, can it be handled as any other normal element? Eg.: Set A={∅, {∅}}, P(A) = {∅, {∅}, {{∅}} {∅,{∅}}}; {∅}U...