a.inc(1) - 4 , so 3 / 16 = 81.) A5: For each of the...

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MAS3300 Exam-A Prof. JLF King 4Jun2008 Note. This is an open brain, open ( pristine ) Sigmon- Notes exam. Please write each solution on a separate sheet of paper. Please be sure to write expressions unam- biguously e.g, the expression “1 /a + b ” should be bracketed either [1 /a ]+ b or 1 / [ a + b ]. Be careful with negative signs! A1: Thm1.4f:(P.2) If c R then c · 0 = 0 . A2: 1.4h:(P.2) If b R then [ 1] · b = b . A3: Prove the triangle ineq., Thm1.20g:(P.6) If x,y R then | x | + | y | > | x + y | . A4: [ Show no work] Write, as a union of open intervals, the set of x R such that 8 x < x 2 + 15. Set= ............................................. . Binops (Binary operators). On R define binops U and D (Up,Down) by b,c R : b U c := Max( b,c ); b D c := Min( b,c ) . So 5 U 7 = 7 and 5 D 7 = 5. On R + = ( 0 , ) define binop / by b,c R + : b / c := b log( c ) . (Here log is base 2; so log(16) = 4 and log( 1 32 ) = 5. E.g, 3 / 16 = 3 log(16) = 3
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Unformatted text preview: 4 , so 3 / 16 = 81.) A5: For each of the following statements in quotes, provide a proof or a CEX with explicit numbers . Recall that axiom DMA (P.1) says that multiplica-tion distributes over addition. a Addition distributes over multiplication. b Binop D distributes over U . c Binop / is commutative. d On R + : Binop / left-distributes over multipli-cation. End of Exam-A A1: 50pts A2: 45pts A3: 55pts A4: 30pts A5: 40pts Total: 220pts Print name ............................................. Ord: Honor Code: I have neither requested nor received help on this exam other than from my professor (or his colleague) . Signature: ............................................
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