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Unformatted text preview: COT 3100 Discrete Mathematics HW #4 Solutions Section 1.7 3. Proof: If x ≥ y, then max(x,y)=x, min(x,y)=y. Thus max(x,y)+min(x,y)=x+y. If x<y, then max(x,y)=y, min (x,y)=x. Thus max(x,y)+min(x,y)=x+y. In either case, max(x,y)+min(x,y)=x+y holds. 4.Proof: If a ≤ b and a ≤c, b ≤c , min(a,min(b,c))= min(a,b)=a. min(min(a,b),c)=min(a,c)=a. If a ≤ b and a ≤c, b >c , min(a,min(b,c))= min(a,c)=a. min(min(a,b),c)=min(a,c)=a. If b ≤a and b ≤c, a ≤c , min(a,min(b,c))= min(a,b)=b. min(min(a,b),c)=min(b,c)=b. If b ≤ a and b ≤c, a >c , min(a,min(b,c))= min(a,b)=b. min(min(a,b),c)=min(b,c)=b. If c ≤a and c ≤b, a ≤b , min(a,min(b,c))= min(a,c)=c. min(min(a,b),c)=min(a,c)=c. If c ≤ a and c ≤b, a >b , min(a,min(b,c))= min(a,c)=c. min(min(a,b),c)=min(b,c)=c. 5 . Proof: Since  ¡ ¢  ¡ £ ¡ , we have ¤¥ ¦ §¨ © ¢ © ¦ ¡ © ¦ ª ¡ £ © ¦ ¡ © ¦ ª ¡ ¢ ¥ ¦ § © ....
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This note was uploaded on 01/22/2012 for the course COT 3100 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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