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Unformatted text preview: { 1 , 2 , 3 }{ 1 , 2 , 3 } and draw its diagram: (( x 1 ,x 2 ) , ( y 1 ,y 2 )) R if and only if x 1 &lt; x 2 , or x 1 = x 2 and y 1 y 2 . 1 (Such an order is called the lexicographic order .) 4. Prove that the following relation on the set of all nonempty subsets of { a,b,c,d } is an order, draw its diagram, nd all the maximal, minimal, least and greatest elements: ( x,y ) R if and only if x y. 5. Determine whether or not the following relations are functions. If a relation is a function, nd its range. (a) { ( x,y )  x,y Z , y = x 2 + 7 } , a relation from Z to Z ; (b) { ( x,y )  x,y R , y 2 = x } , a relation from R to R . 6. For each of the following functions, determine whether it is onetoone and determine its range. (a) f : Z Z , f ( x ) = 2 x + 1; (b) f : Q Q , f ( x ) = 2 x + 1; (c) f : Z Z , f ( x ) = x 3x ; 2...
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This note was uploaded on 12/12/2010 for the course MACM 201 taught by Professor Marnimishna during the Fall '09 term at Simon Fraser.
 Fall '09
 MarniMishna

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