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# CMSC 150 Fall 2015 Section 7981 - Assignment 1 | Complete Solution

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**CMSC 150 Fall 2015 Section 7981 - Assignment 1, due October 25**

In this assignment, **N** will denote the set of positive integers, **Z** the set of all integers, **Q** the set of all rational numbers, and **R** the set of all real numbers. After any problem statement, feel free to hit the Enter key as often as you need to make space for your answer.

**Problem 1:** Let *A* = {3,5,7}, *B*={2,3}, *C* = {1,2,3,4,7}. Compute the following sets:

*A* Ç *B* =

*A* È *B* =

*A* – *B* =

*B* – *C* =

*A* Å *C* =

*A* ´ *C* =

**Problem 2:** Let *D* = {5, 2, {5,2}, {5, {2}}, {{*a*,*b*,*c*},{*c*,*d*,*e*}}} How many elements does *D* have?

**Problem 3:** A set *E* has 37 elements. How many subsets does it have? (An answer correct to 5 significant digits will be acceptable.)

**Problem 4:** In 24x7 Section 1.4, the author states “The null set f is a proper subset of every set.” Is this correct or incorrect? Explain.

**Problem 5:** List the elements in the set { *x* Î **Z** | *x*^{2} – 7*x* + 5 = 0 }.

**Problem 6:** Let *M* = { *y* Î **Q** | 0 < *y* <= 1, and *y* can be written as a fraction with a denominator not exceeding 6. } List all the elements of *M*. How many elements are there in *M*?

**Problem 7:** How many elements are there in the set {{{{{{{3}}}}}}} ?

**Problem 8:** Let Ã(*X*) denote the power set of *X*. Find Ã({*a*, *b*, *c*, *d*}).

**Problem 9:** For each positive integer n, define the set *An* by *An*= {*x *Î **Z** | *n* £ *x* £ 2*n*}

a. What is the union of all sets *An*?

b. What is the intersection of all sets *An*?

**Problem 10:** For every real number *x*, define *Bx* to be the open interval (-*x*,*x*). Equivalently, *Bx* = {*y* Î *R* | |*y*| < *x*}.

a. What is the union of all sets *Bx*?

b. What is the intersection of all sets *Bx*?

**Problem 11:** Simplify each of the following algebraic expressions. All sets are assumed to be subsets of a universal set **U**.

a. (*A* È *B*) Ç (*C* È *A*)

b. (*A* È f) Ç *A*

c. (*A* È *B*) Ç (*A* Ç *B*)

d. *A* È (**U** – *A*)

## [Solved] CMSC 150 Fall 2015 Section 7981 - Assignment 1 | Complete Solution

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