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quizzes-SELO

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

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Sets&Logic 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 · n 5 x 2 | {z } E 1 | {z } E 2 E 1: . . . . . . . . . . . . E 2: . . . . . . . . . . . . E 3: . . . . . . . . . . . . Q5: ( Fri, 25Sep ) i Stmt C B has contrapositive . . . . . . . . . . . . . . . . . . . . and converse . . . . . . . . . . . . . . . Recall & , , ¬ mean And, Or, Not . Using only & , , ¬ , 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 P ( S ) = . . . . . and P ( P ( S ) ) = . . . . . . . . . . . . . . . . . . . Q7: ( Fri, 9Oct ) The mod-13 reciprocal of 5 is . . . . . . . . . . . Q8: ( Wed, 14Oct ) a Repeating decimal 3 . 1 41 equals n d , where posints n d are n = . . . . . . . . . . . . . . . and d = . . . . . . . . . . . . . . . . b Writing 167 / 111 as a repeating decimal gives 167 111 = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Q9: ( Fri, 23Oct ) The number of ways of having 9 objects from 4 distinct types is s 9 4 { Binom === coeff . . . . . .

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

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