quizzes-SELO.2011t

quizzes-SELO.2011t - Sets&amp;amp;Logic Q1: Wed. 7 Sep α...

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Unformatted text preview: Sets&Logic Q1: Wed. 7 Sep α Q6: Fri. Deﬁne fncs G,F :[1 .. 12] , where G(n) is the 30 Sep Sept2011 Quizzes Q A map f : Ω→Λ is an involution if number of letters in the nth Gregorian month [so G(2) = 8; the 2nd month “February” has 8 letters], and F (n) := 13 − n. ..... [Imagine 2 blank lines]. .................................................. β Write the truth-table for B ∨ [¬B ]⇒C . Q2: Fri. 9 Sep i A formal defn of y •| z , i.e “y divides z ”, is: ii On Z, say that x Trans. T rn 0 1 qn 1 0 23 0 1 2 3 4 5 · 100] + [ · 23]. So the soln to ...... ...... congruence 23x ≡100 8 is x= ∈ [0 .. 100). ................ Thus 1 = [ Q4: Fri. Mod M :=71, the recipr. 16 Sep 1 23 M = [Hint: ] So x= solves 4 − 23x ≡M 1. .......... ∈[0 .. M ) .... ∈[0 .. M ). Q5: Wed. 21 Sep α Mod M :=174, the recipr. [Hint: ] So x= .......... 1 55 M = ∈[0 .. M ) F. Q8: tn 100 y IFF x − y Symm. T F T strike this table! (I.e, please ﬁll sn F. Symmetric T ........ ∈[0 .. M ). solves 4 − 55x ≡M 6. β For each index k , the k th -row in LBolt satisﬁes (ITOf the r, q, s, t vars) equation: [Subscripts readable!] . ...................................................... F. 1. Then Reﬂex. T is: F. (Be careful on both parts!) in.) n Q7: Mon. On Z+ , write x \$ y IFF xy < 0. So \$ is 17 Oct F T If b •| c and x •| y , must [b + x] •| [c + y ] ? Q3: Wed. May lightning 14 Sep . ..................................................... Let ϕ := F ◦ G. Then ϕ◦2 (11)= . .................... F. Reﬂexive T F. .................................................. .................................................. If b •| c and b |• c, must b = c ? is Transitive T [Hint: What kind of objects are y, z ? What QFR(s) do you need?] ii The set of posints k with G◦k (1) = G◦k (2) Wed. 19 Oct ? lems. Solve all of the World’s Prob- ...
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