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# 离散结构课业代写 CS 2100代写

2022-09-15 11:47 星期四 所属： CS代写 浏览：31 ## Homework 3

### 1.Exercise 2.a on page 193.

Let A = {x ∈ N: x = 4k for some k ∈ N}, B = {y ∈ Z : 2y is a perfect squareu}, and C = {z ∈ Z : z2 ﹤ 1, 000}. List five elements in the following set: A ∪(B C).

### 2.Exercise 16.b on page 195.  离散结构课业代写

Use Venn diagrams to verify the following property of our set operations:

One of DeMorgan’s laws:

(A B)’ = A’ ∩ B

### 3.Exercise 18.b and 18.e on page 195.

Given A = {2x : x ∈ Z} and B = {3y : y ∈ Z}, describe each of the following using the simplest set-builder notation possible:

(a) A – B

(b) Z – A

### 4.Exercise 1.b on page 209.  离散结构课业代写

Given the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and set A = {2, 4}, B = {1, 2, 8}, and C = {1, 2, 5, 6, 10}, find the following:

(A × B) ﹣ (A × A)

### 5.Exercise 9 on page 209.

Let A = {2k : k ∈ Z}, B = {4k ＋ 1 : k P Z}, and C = {4k ＋ 3 : k ∈ Z}. Explain why {A, B, C} is a partition of Z.

### 6.Exercise 2.e on page 219.  离散结构课业代写

Prove the following statement about specific sets:

({2n ＋ 1 : n ∈ Z} ∩ {5m ＋ 4 : m ∈ Z}) ⊆ {10k ＋ 9 : k ∈ Z}

### 7.Exercise 11.d on page 220.

Give an element-wise proof for the following:

If A B = B and B C = C , then A C = C.

### 8.Exercise 13.c on page 220.  离散结构课业代写

Give an element-wise proof for the following:

If A ⊆ B , then A ∪ (B – A) = B.

### 9.Exercise 14.e and 15.e on page 220.

Consider the following equation:

(A B) ∩ (A’ X C)’ = A ∪ (B C’)

(a) Prove the equation by quoting the appropriate parts of Theorem 6.

(b) Form the dual of the equation.

### 10.Exercise 22.a on page 221.  离散结构课业代写

Prove the following statement:

(A B) × C = (A × C) ∩ (B × C) ### 关键字： 