Please help me out with a few questions for Discrete Mathematics. It would reall

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Please help me out with a few questions for Discrete Mathematics. It would really help me if you provide the explanations for them as well. Thank you.

Determine which of the following are true and which are false. Explain your answers. The power set of a set A is the set of all subsets of A. For A = {1,2,3,4}, find Let A = . Find P(A). How many elements are in P(A)? Let A = {a}. Find P(A). How many elements are in P(A)? Find P(P(A)). How many elements are in P(P(A))? Show that the statement in #12a(in section 2.1 of the textbook) is false by exhibiting a counterexample. Section 2.2: Let A = {0,1,2,3,4,5,6}. Find: {n A : n 5} {2m + 1 : m A} {n A : n = 2k for some k z}

Explanation / Answer

Answers

1(a) True bcz a is one element of set {a,b,c}

1(b) False bcz a is not a set

1(c) False {a} is not element

1(d) True {a,b} is a subset

1(e) True {a,b} is a subset

1(f) True ? is a subset of any set

1(g) True 4 is greater than 3

1(h) False 5 is not sum of 2 even no's

2(a) A= { }

2(b) A= { {1},{2}, {3},{4}}

2(c) A={{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

2(d) A ={{1,2,3},{1,3,4},{2,3,4}}

2(e) A= {1,2,3,4}

3. p(A) ={ } no. of elements are zero

4. P(A)= {{},{a}} No of elements in P(A) are 2, P(P(A))= {{},{a},{{},{a}} b No of elements in P(P(A)) are 3

Section 2.2

1(a) {5,6}

1(b) {0,1,2}

1(c) {2,4,6}

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