Chapter 3-1 Relations and Ordered Pairs

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Chapter 3-1 Relations and Ordered Pairs

• Alg. 2 Notes

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Cartesian Product

• A x B means The product (x) of sets A and B
• is the set of all ordered pairs having the 1st
• member from set A and the 2nd from set B.

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Example 1

• Find the Cartesian product Q x Q , where Q
  2,3,4
• Answer
• (2,2), (2,3), (2,4),(3,2), (3,3), (3,4),(4,2),
  (4,3), (4,4)
• Notice a 3 x 3 Set has 9 elements!!

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Example 2

• Find the cartesian product A x B where set
• A stinky, farty
• B Carl, James, Cody
• Answer
• (stinky,Carl),(stinky, James), (stinky, Cody)
• (farty,Carl), (farty,James), (farty, Cody)
• Notice a 2 x 3 product has 6 elements!!

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Domain and Range

• Domain (x) the set of all the first members
• Range (y) the set of all the second members

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Example 3

• List the domain and range of the relation (a,1),
  (b,2), (c,3), (e,2)
• Answer
• Domain a,b,c,e
• Range 1,2,3, Notice repeated elements not
  listed twice

When you list individual elements it is called
roster notation
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Set Builder Notation

• x I x ? 3 read as the set of all x such that
  x is less than or equal to 3
• Example 4
• Use the set 1,2,3,,10 to find x I 4 lt x lt 7
• Answer
• 5,6

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Example 5

• Let Q 2,3,4 (Ex 1)
• Use Q x Q to find (x,y) x lt y
• (read Use the cartesian product of Q to find
  members such that the x-value is less than the
  y-value.
• Answer

• (2,3), (2,4), (3,4)

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Example 6 You Try

• Use the relation R x R where R 1,3,5,7.
• Find (x,y) I y x 2