quizzes-SELO - Sets&Logic 4Sept2009 Quizzes Q Using...

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Quizzes Q 4Sept2009 Q1: ( Fri, 4Sep ) Let τ () and σ () be the number-of and sum-of divisors, resp. . Then τ (2700) = ............... and σ (2700) = ................................ . ( Please leave each answer as a product of three integers. ) Q2: ( Fri, 11Sep ) a Write 27 2009 7 . ( i.e, working mod 7 ) and 9 35 7 ................ , each as a value in [ 0 .. 7 ) . b If 5 K •|| 1000, then K = ......................... . Q3: ( Wed, 16Sep ) May lightning strike this table! ( I.e, please fill in. ) n r n q n s n t n 0 100 1 0 1 23 0 1 2 3 4 5 Thus 1 = [ ...... · 100] + [ ...... · 23]. So the soln to congruence 23 x 100 8 is x = ................ [ 0 .. 100 ) . Q4: ( Wed, 23Sep ) a Write the name of each symbol: b floor d ceiling h .............. { .............. [ .............. . b Write the free vars in each of these expressions. E 3 z }| { n N : f ( n ) < [ r +7 = r - 4 ± x Z ² ² · n 5 x 2 ³ | {z } E 1 | {z } E 2 E 1: ........... . E 2: ........... . E 3: ........... . Q5: ( Fri, 25Sep ) i Stmt C B has contrapositive .................... and converse .............. , , ¬ mean And, Or, Not . , , ¬ ,B,C , write C B as .............. . ii Let B :=39 ,M :=105 ,T :=3 . Cgr B · x M T has reduced Cgr β · y μ τ , where β = ................................ , μ = ....... , τ = ..... , and soln y = ....... [ 0 ..μ ) . Cgr B · x M T , has ... many solns, which are x = .................................... [ 0 ..M ) . Q6: ( Mon, 05Oct ) a ϕ (121000) = ................... . Express your answer as a product p 1 e 1 · p 2 e 2 · ... of primes to posint powers, with p 1 < p 2 < ... . b ( With P () the powerset operator, let S := 3-stooges. ) Then ² ² P ( S ) ² ² = ..... and ² ² P ( P ( S ) ² = .................. . Q7:
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quizzes-SELO - Sets&amp;Logic 4Sept2009 Quizzes Q Using...

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