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# CMSC 150 Fall 2015 Section 7981 - Assignment 1 use as a guide only

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- NUMBER1TUTOR
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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 B=

AB=

A–B=

B–C=

AC=

AC=

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 is a proper subset of every set.”

Is this correct or incorrect? Explain.

Problem 5: List the elements in the set { x Z | x2 – 7x + 5 = 0 }.

Problem 6: Let M = { y 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 (X) denote the power set of X. Find ({a, b, c, d}).

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

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 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 B) (C A)

b. (A ) A

c. (A B) (A B)

d. A (U – A)

## [Solved] CMSC 150 Fall 2015 Section 7981 - Assignment 1 use as a guide only

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- Submitted On 12 Dec, 2015 08:01:02

- NUMBER1TUTOR
- Rating : 87
- Grade :
**A+** - Questions : 0
- Solutions : 5075
- Blog : 3
- Earned : $14642.59