Answer to Question #171728 in Discrete Mathematics for Mary-Ann Asuncion

Question

^{A. Find the indicated sets.}

2.ℙ({1,2,3,4})

6. ℙ({1,2})x ℙ({3})

10.  {Xϵ ℙ({1,2,3}):│X│≤1}

B. Suppose that │A│=m and │B│=n. Find the following cardinalities.

14. │ ℙ(ℙ(A))│

18. │ ℙ(Ax ℙ(B))│

Answer 1

(2) Number of elements = 4

So power of set= 2ⁿ = 2ⁿ = 16

P({1,2,3,4})=16

(6) P({1,2}) =2ⁿ=4 and P({3}) =2ⁿ=2

P({1,2})×P({3})=4×2=8

(10)

P({1,2,3})=2³=8

(14) |P(P(A))|= 4

P(A)= 2¹=2

P(P(A)) = 2²=4

(18) P(B) = 2¹= 2

A× P(B) = 1 × 2 = 2

P(A×P(B))= 2²= 4