9 BINARY RELATIONS - tmarris.com

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109.10 INVERSEWe introduce as a given type DRINK, the set of all drinks.[ DRINK ]We define costs as a binary relation from drink to price.costs : DRINK j Zcosts = { tea å 50, coffee å 75, hotChocolate å 75, soup å 75 }So, for example, tea costs 50 pence.If we reversed the binary relation, if we made it from price to drink and called it buys, so, forexample, 50 pence buys tea:buys : Z j DRINKthenbuys = { 50 å tea, 75 å coffee, 75 å hotChocolate, 75 å soup }buys is the inverse of costs. We write:costs~ = buys(say costs inverse equals buys). ~ (tilde) is the inverse operator. The inverse of a binary relation isanother binary relation with the coordinates of their ordered pairs reversed.
11EXERCISE 9.81 We introduce the type NAME, the set of all people's names, and definealias : NAME j NAMEalias = { tom å dopey, sam å dozy, stu å dreamy, tom å sleepy, sam å titch }Evaluate:a alias~b alias t { dozy, dreamy }c alias · { tom, sam } ‚d alias · { sue } ‚e alias~ · { dreamy, dozy } ‚
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9 BINARY RELATIONS - tmarris.com

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