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CH1 - Chapter 1 Speaking Mathematically Section 1.1 6 a s...

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Chapter 1: Speaking Mathematically Section 1.1 6. a . s is negative b . negative; the cube root of s is negative ( Or : 3 s is negative) c . is negative; 3 s is negative ( Or : the cube root of s is negative) 9. a . have at most two real solutions b . has at most two real solutions c . has at most two real solutions d . is a quadratic equation; has at most two real solutions e . E has at most two real solutions Section 1.2 6. T 2 and T - 3 each have two elements, and T 0 and T 1 each have one element. Justification : T 2 = { 2 , 2 2 } = { 2 , 4 } , T - 3 = {- 3 , ( - 3) 2 } = {- 3 , 9 } , T 1 = { 1 , 1 2 } = { 1 , 1 } = { 1 } , and T 0 = { 0 , 0 2 } = { 0 , 0 } = { 0 } . 9. c . No: The only elements in { 1 , 2 } are 1 and 2 , and { 2 } is not equal to either of these. d . Yes: { 3 } is one of the elements listed in { 1 , { 2 } , { 3 }} . e . Yes: { 1 } is the set whose only element is 1. g . Yes: The only element in { 1 } is 1, and 1 is an element in { 1 , 2 } . h . No: The only elements in {{ 1 } , 2 } are { 1 } and 2, and 1 is not equal to either of these. j . Yes: The only element in { 1 } is 1, which is is an element in { 1 } . So every element in { 1 } is in { 1 } . 12. All four sets have nine elements. a . S × T = { (2 , 1) , (2 , 3) , (2 , 5) , (4 , 1) , (4 , 3) , (4 , 5) , (6 , 1) , (6 , 3) , (6 , 5) } b. T × S = { (1 , 2) , (3 , 2) , (5 , 2) , (1 , 4) , (3 , 4) , (5 , 4) , (1 , 6) , (3 , 6) , (5 , 6) } c . S × S = { (2 , 2) , (2 , 4) , (2 , 6) , (4 , 2) , (4 , 4) , (4 , 6) , (6 , 2) , (6 , 4) , (6 , 6) } d. T × T = { (1 , 1) , (1 , 3) , (1 , 5) , (3 , 1) , (3 , 3) , (3 , 5) , (5 , 1) , (5 , 3) , (5 , 5)
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