Sets Homework Problems

Complete the Following Problems

Be sure to show all work, where possible. If work can’t be shown, a verbal explanation of your reasoning works just fine. Submit your written work through your class’s Learning Management System (such as Blackboard, Canvas, etc.)

1.) True or False: \(3\in \{1,3,4,5,6,7,11,100\}\)

2.) True or False: \(3.14 \in (0,4)\)

3.) True or False: \(2\in (2,10]\)

4.) True or False: \(3\in [3,7]\)

5.) True or False: \(\{2,3,5\}\in \{1,2,3,\{2,3\},\{2,3,5\}\}\)

6.) True or False: \(\{1,2,3\}\in \{1,2,3,4,5\}\)

7.) True or False: \(5 \in \{x:\ x\in\mathbb{N},\ and\ 2\leq x\leq 7\}\)

8.) True or False: \(\{1,2,3\}\subseteq \{1,2,4,5,6\}\)

9.) True or False: \(\{1,2,3\}\subseteq \{1,2,4,3, 7,10\}\)

10.) True or False: \(\{2,4\}\subseteq \{2n | n\in \mathbb{N},\ and\ n>3\}\)

11.) True or False: \(\{1,4,5\}\subseteq (0,10)\)

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For problems 12-19, let \(U=\{0,1,2,…,9,10\}\) be a universal set, and

\(A=\{1,3,4,5,7\}\), \(B=\{2,4,5,6,11,12\}\) and \(C=\{2,3,4,6\}\).

12.) Compute \(A\cup B\)

13.) Compute \(B\cap C\)

14.) Compute \(\overline{C}\)

15.) Compute \(A\setminus B\)

16.) Compute \((A\cap B)\cup C\)

17.) Compute \((\overline{C}\cap B)\cup C\)

18.) Compute \((A\cap B)\cap \overline{A}\)

19.) Compute \((A\setminus B)\setminus C\)

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20.) Let \(I=(0,4)\) and \(J=[2,6]\). Compute \(I\cup J\) and draw the answer on a number line.

21.) Let \(I=(0,4)\) and \(J=[2,6]\). Compute \(I\cap J\) and draw the answer on a number line.

22.) Let \(I=[-1,1]\) and \(J=[3,5]\). Compute \(I\cup J\) and draw the answer on a number line.

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For problems 23-25, let \(A=\{0,1\}\), \(B=\{2,3,4\}\) and \(C=\{1,2\}\).

23.) Find \(A\oplus B\)

24.) Find \(B^2\)

25.) Find \(C\oplus A\oplus B\)

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26.) Let \(A=\{2,4, 6,10\}\) Find \(|A|\).

27.) Let \(B=\{1,4,\{2,3,4\},\{4,5\}, \{7,8,9\}\}\). Find \(|B|\)

28.) Let \(N=\{n:\ n\in \mathbb{N}\ and\ 3\leq n \leq 15\}\). Find \(|N|\)