Answer:
What is the cardinality of A? 4
What is the power set of ℘(A)?
P(A) = {Ф, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {b,c,d}, {a,c,d},{a,b,c,d}}
What is the cardinality of the power set? 16
What is the power set of A = { }? => {{ }} or {Ф
Explanation:
Given set is:
A = {a,b,c,d}
What is the cardinality of A?
The cardinality of set is the number of elements in the set
Since, set A has four members the cardinality is 4.
i.e.
n(A) = 4
What is the power set of ℘(A)?
The power set of a set consists of all the subsets of a set.
So the power set of A will consist of all subsets of A.
The power set is:
P(A) = {Ф, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {b,c,d}, {a,c,d},{a,b,c,d}}
What is the cardinality of the power set?
The number of subsets of a set is the cardinality of power set.
As A is 4 members,
Cardinality of Power set of A = 2^4 = 16
What is the power set of A = { }
As A is an empty set, its power set will have only one element (Ф) as member
P(A) = {{ }} or {Ф}
Hence,
What is the cardinality of A? 4
What is the power set of ℘(A)? P(A) = {Ф, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {b,c,d}, {a,c,d},{a,b,c,d}}
What is the cardinality of the power set? 16
What is the power set of A = { }? => {{ }} or {Ф
