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Set Theory

Set Theory. A1 Set Notation. Set Notation. Only what is listed. <. Ends are NOT included. ≤. Ends ARE included. Set Notation. Example 1: Write the following in interval notation a. 0 < x ≤ 5 ____________ b. 0 ≤ x < 5 ____________ c. 0 ≤ x ≤ 5 ____________

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Set Theory

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  1. Set Theory A1 Set Notation

  2. Set Notation Only what is listed < Ends are NOT included ≤ Ends ARE included

  3. Set Notation Example 1: Write the following in interval notation a. 0 < x ≤ 5 ____________ b. 0 ≤ x < 5 ____________ c. 0 ≤ x ≤ 5 ____________ d. 0 < x < 5 ____________ ( 0, 5 ] [ 0, 5 ) [ 0, 5 ] ( 0, 5 )

  4. Set Notation Example 2: Write the following in interval notation: the set of all numbers… a. greater than 0 and less than 5 b. greater than or equal to 0 and less than 5 c. greater than 0 and less than or equal to 5 d. from 0 to 5 inclusive ( 0, 5 ) [ 0, 5 ) ( 0, 5 ] [ 0, 5 ]

  5. Set Notation { 1, 2, 3, 4, 5 ? } { 0, 1, 2, 3, 4 , 5 } ? 0 0 Is NOT included IS included 5 5 Is NOT included IS included

  6. Examples 3. List all the elements of the set a. {x| -3 < x <3; x is an integer} _____________________ b. {x| -2 ≤ x < 3; x is an integer} _____________________ c. {x| -2 ≤ x ≤ 2; x is an integer} _____________________ d. {x| -3 < x ≤ 2; x is an integer} _____________________ { -2, -1, 0, 1, 2 } { -2, -1, 0, 1, 2 } { -2, -1, 0, 1, 2 } { -2, -1, 0, 1, 2 }

  7. Examples 4. Which set builder notation represents {-2, -1, 0, 1, 2}? a. {x| -3 ≤ x ≤ 2, where x is an integer} b. {x| -3 < x ≤ 3, where x is an integer} c. {x| -2 < x < 2, where x is an integer} d. {x| -2 ≤ x < 3, where x is an integer} X X X c. Says that -2 d. Says that -2 d. Says that 3 b. Says that 3 b. Says that -3 a. Says that -3 IS in there is NOT in there is NOT in there Is NOT in there IS in there IS in there True? True? True? True? True? True? No Yes No No Yes Yes

  8. Examples 5. Which set builder notation represents {1, 3, 4, 7, 9, 11, 13}? a. {x| 1 < x < 13, where x is a prime number} b. {x| 1 ≤ x ≤ 13, where x is a prime number} c. {x| 1< x < 13, where x is an odd integer} d. {x| 1 ≤ x ≤ 13, where x is an odd integer} X X X Says that 1 is NOT in there. What is a prime number? Can only be divided by 1 and itself 1 2 2? 3? 3 5 4? 7 9? 11 13

  9. Examples 6. Written in set builder notation, S = {1, 2, 3, 5, 7} is a. {x| 0 < x < 10, where x is an odd integer} b. {x| 0 ≤ x ≤ 10, where x is an odd integer} c. {x| 0 < x < 10, where x is a prime number } d. {x| 0 ≤ x ≤ 10, where x is a prime number } X X

  10. Practice Problems Now try the practice problems on your own

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