The discussion focuses on demonstrating that the set ##\{ \{x\}, \{x,y\} \}## is an element of the power set of the power set of set ##B##, denoted as ##\mathcal{P} \mathcal{P} B##. It establishes that since both ##x## and ##y## are members of set ##B##, the individual sets ##\{x\}## and ##\{x,y\}## are subsets of ##B##. Consequently, by the definition of a power set, the set ##\{ \{x\}, \{x,y\} \}## qualifies as a subset of the power set of ##B##, confirming that ##\{ \{x\}, \{x,y\} \} \in \mathcal{P} \mathcal{P} B##.
PREREQUISITESStudents of mathematics, particularly those studying set theory, educators teaching foundational concepts in mathematics, and anyone interested in formal proofs involving subsets and power sets.
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 ...