Page 11 - Discrete Structure II

Example

Let B = {3, 5, 8} what it the power set of B?

Answer:

P(B) ={∅, {3}, {5}, {8}, {3, 5}, {5, 8}, {3, 8}, {3, 5, 8}}
Exercise

A = { a, b, c, d} , what is the power set of A?

P(B) = { ∅, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, { b, c}, {b, d}, {c, d}, {a, b, c}, {a, c, d}, {b, c, d}, {a, b, d}, {a,
b, c, d}}

D = { a, b} P (D) = {∅, {a}, {b}, {a, b}}

Exercise

Which of the following is true? Given the set A = {a, b}

1. P (A) = {∅, {a}, {a, b}, {b} }
2. ∅ ∈ A
3. ∅ ∈ P (A)
4. ∅ ⊂ A

5. ∅ ⊂ P (A)
6. {a} ∈ A
7. ∅ ∈ P (A)
8. {a} ⊂ A
9. {a} ⊂ P (A)

Answer:

1. P (A) = {∅, {a}, {a, b}, {b} }

True, the order of elements in a set does not matter.

2. ∅ ∈ A

False, because ∅ is a subset of A, not an element of A