{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–2. Sign up to view the full content.

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)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}