Oh, right. That seems really obvious now. So the power set of B is the set of all subsets. Since ##\{x\}## and ##\{x,y\}## are subsets of B, the set ##\{ \{x\}, \{x,y\} \}## must be a subset of the power set.FactChecker said:If something seems obvious, just see if you can use the basic definitions to state it. State the definition of power set and start there.
Since x and y ∈ B, {x} and {x,y} are subsets of B. By the definition of the power set ...
Set theory is a branch of mathematics that deals with the study of sets, which are collections of objects. It is used to define and analyze the relationships between sets and their elements.
A subset relationship in set theory refers to the relationship between two sets, where every element in one set is also an element in the other set. In other words, if set A is a subset of set B, then all elements in A are also present in B.
If x and y are elements of set B, it means that they are individual objects or values that are part of the set B. In other words, they are members of set B.
The subset relationship is represented using the subset symbol, which is ⊆. It is placed between the two sets, with the subset set being on the left side of the symbol and the superset on the right side. So, if A is a subset of B, it would be written as A ⊆ B.
A proper subset is a subset relationship where the subset is not equal to the superset. This means that there is at least one element in the superset that is not present in the subset. An improper subset, on the other hand, is a subset relationship where the subset is equal to the superset. This means that all elements in the superset are also present in the subset.