Question

Use the set A = { a, b, c ,d } to answer the following questions.

Answer 1

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