The null set. It is a subset of every set.
The null set. Every set is a subset of itself and so the null set is a subset of the null set.
Yes the null set is a subset of every set.
No. The null set cannot have a proper subset. For any other set, the null set will be a proper subset. There will also be other proper subsets.
yes!
The null set. It is a subset of every set.
I was told once that the null set is the compliment to the universal set... I'm not convinced of this, however because the null set is a subset of the universal set as well. While I can't think of anything offhand that would prevent both of these statements from being true, it seems to me that they are contradictory statements.
yes
Yes. A null set is always a subset of any set. Also, any set is a subset of the [relevant] universal set.
The null set. Every set is a subset of itself and so the null set is a subset of the null set.
Yes the null set is a subset of every set.
yes
No. The null set cannot have a proper subset. For any other set, the null set will be a proper subset. There will also be other proper subsets.
yes!
A - B is null.=> there are no elements in A - B.=> there are no elements such that they are in A but not in B.=> any element in A is in B.=> A is a subset of B.
The definition of subset is ; Set A is a subset of set B if every member of A is a member of B. The null set is a subset of every set because every member of the null set is a member of every set. This is true because there are no members of the null set, so anything you say about them is vacuously true.
The null hypothesis for a 1-way ANOVA is that the means of each subset of data are the same.