Question

Consider the set b = { ∅ , a, {a}, { {a} } }. the number of elements in p(b) is _____. A) 8 B) 6 C) 4 D) 16 E) 2

Answer 1

`D`

Explanation:

In discrete mathematics, set
`A` is a subset of set
`B` if all the elements of
`A` are also elements of
`B`. Power set
`P(S)` of set
`S` is the set of all the subsets of
`S`, including the empty set and
`S` itself. The cardinality
`|S|` of set
`S` is a measure of the number of elements of set
`S`. Given
`B = \{\emptyset, a, \{a\}, \{\{a\}\}\}`,
`|P(B)|`, that is the cardinality of our power set
`P(B)`, is equal to
`2^n` where
`n` denotes the number of the elements in
`P(B)`:
`|P(B)| = 2^4 = 16`. To be more precise,
`P(B) = \{\emptyset, \\ \{\emptyset\}, \{a\}, \{\{a\}\}, \{\{\{a\}\}\}, \\ \{\emptyset, a\}, \{\emptyset, \{a\}\}, \{\emptyset, \{\{a\}\}\}, \{a, \{a\}\}, \{a, \{\{a\}\}\}, \{\{a\}, \{\{a\}\}\}, \\ \{\emptyset, a, \{a\}\}, \{ \emptyset, a, \{\{a\}\}\}, \{\emptyset, \{a\}, \{\{a\}\}\}, \{a, \{a\}, \{\{a\}\}\}, \\ \{\emptyset, a, \{a\}, \{\{a\}\}\}\}`.