# 2nd-06 - we Mathematical Structures second Mid ‘Term Exam...

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Unformatted text preview: we Mathematical Structures second Mid- ‘Term Exam if 18/12/05 L . - j i . - l. q ﬂProve that 22:1 1:2 = .n(n + 12:2” + 1) for all n 2 1. e the Law of Set Theory to prove the equality m A\(Bn0)=(A\B)U(,A\C) l for all subsets A, B, C of the universal set‘U. Illustrate this set A L with a Venn Diagram. q={(\$,y)lw,yeA, [email protected]}- “all; L .¢ (a; Represent p and q as directed graphs and as matriées.. (lea Find the relation and represent it as a matrix. _ (13’ Find the relation 9 and represent it as a directed graph. ' ( \ ”Let f be a function on A = {(1, b, c ‘ 4% ﬁg)»; X_ - f(d) = b. * 4,; we . \,\om?ndfl~b)a“dflclm=- . . . 4 kg), .(RA nth (b) 1-?in f(b) and f(c) 1% . z__1_s the identity function). a r \g n ' V we r, Solve the recurrence relation SOC) '—S'(l<:—l) —6S(k; —.2) = Gk— l h ’ 2.x i_ with initial conditions 3(0) = 1, 5(1'3 = 1 (Hint: Use ak + b as your trial solution). ‘ {W) H C)»: 0’ W“ '3, , {icicle a” Kg .- / ,r' I H ,5 w M , v. ' . “I N! "ix/ \ . {019(9) a K0 — Y4? - __ . . :17 g. .'__ C, ' {a I [lull-v.1“. v . ., -/ ‘2". ‘ A ' 1',“ (“'5‘ ":1 I ‘5 . ll: ' “’1'.- ( it ‘ “"3; ,. I .‘ 2 3 ,4 4' ,7 j a is «’7 , I I] V _.J n _ >4“ LL ’ \2 '1 J h 9K" / ' <4 . _ J ’4‘ - h. 1 ‘ -. .l x _ ‘ x \0'» l < K it / W N .r I ,2, {— ‘3‘ a 3/ 1.. s :1 \l _ f 4‘ \Qm: \ '1’ .7" K' ‘. V __ ‘ , ,. , \L 4' l ". q” Q} : " f _; "‘» KL. .: .«/ (f. .4, .;\..~.w .- » \(3 \K: 423% ’L _ > ., WE,— . - Iéjmﬁm‘fﬁi’fi‘mmzﬁﬂtimikim»ﬁlth“,f w gs‘IaiEE-&;;V=ﬁilé,"§§\$!£gd:nji4mam u ‘ :-..---.;-.- :Ar-d":|.l.'.w—")J 5W. , . ,.. “.153, 4:4. i... - m- -» ...
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