4 Chapter 1 Real Numbers and Algebraic Expressions Student Check 1 Determine the requested information for the given sets. a. Use the roster method to write the set A = 5xux is a counting number greater than 36. b. Let A = 55, 10, 15, 20, 25, 306 and B = 515, 30, 45, 60, 756. Find A B and A B. c. The following table provides information about the top public colleges according to the Best Colleges Rankings in 2012. (Source: http://colleges.usnews .rankingsandreviews.com/best-colleges/rankings/national-universities/top-public) College Undergraduate Enrollment 2011–2012 Tuition (In State) University of California, Berkeley (UC Berkeley) 25,540 $11,767 University of California, Los Angeles (UCLA) 26,162 $11,604 University of Virginia (UVA) 15,595 $11,576 University of Michigan (U-M) 27,027 $12,590 University of North Carolina, Chapel Hill (UNC) 18,579 $ 7,008 College of William and Mary (W&M) 5,898 $13,132 Georgia Institute of Technology (GT) 13,750 $ 9,652 University of California, San Diego (UCSD) 23,663 $12,128 University of California, Davis (UC Davis) 24,737 $12,794 University of California, Santa Barbara (UCSB) 19,186 $12,508 Let A = 5xux is a college with enrollment less than 20,0006 and B = 5xux is a college with annual cost greater than $12,5006. i. State set A using the roster method. ii. State set B using the roster method. iii. Is UVA ∈ A B? The Real Numbers Numbers are such a critical component of our lives. We use them to represent so many things, such as, the amount of money in our bank account, the hours in a day, the temperature outside, our current weight, our height, the credit hours we are enrolled in, our GPA, our salary, measurements, and so on. Furthermore, computers store all of their data as numbers. The world as we know it would cease to exist without numbers. Numbers belong to certain sets. The following table defines the sets of numbers that make up the real numbers. Natural numbers = {1, 2, 3, 4, 5, . . .} Whole numbers = {0, 1, 2, 3, 4, 5, . . .} Integers = {. . . , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, . . .} Rational numbers = e p q ` p, q with q 2 0 f Irrational numbers = {numbers that are not rational} Real numbers = {rational or irrational numbers} The rational and irrational numbers are discussed in more detail next. Objective 2 ▶ Classify a number as a natural number, whole number, integer, rational number, or irrational number.
hendricks_intermediate_algebra_1e_ch1_3
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