# PracExam2P1 - Math llle{Summer Hessian Kﬂuhs Preetiee...

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Unformatted text preview: Math llle {Summer Hessian} ' Kﬂuhs. Preetiee Essen 2 1-} (2 pts. eeeh) Determine ifeseh ef the feﬂewing statements is true ('1‘) er false [F]! Ne explanatien is necessary. a.) Every relstien is s l‘unetien. _ 11.} Every fun-Men is a reintien. e.) ﬁemliGeF} 2 BMW} ftir ell fenetiees G and F. e} {\$1, {1,2}, {3}} is n pertiﬁen ef {1,2,3}. e.) {(1,21, {2,1}, {2, 3}, {3, 2}, {1, 3}, {3,1}} is symmetric. ﬁll {{11 2]. {3.1i.{2.331. E3. 3}. {l1 3). {3. 1}} is transitive- 2.] [8 pie.) Deﬁne relatien [2 en E, the set ef integers, by st}: il'f 5|{s — :e]. Sher-r that t? 55 it} reﬂexive en 3. h.) symmetric. e} transitive. 3.} {-‘1 pte.) Let A = {1, 2,3,4, 5, I3} and let H = {{1,E}, {3, s1, 5}, {3}} he 3 pnrtitien ef set A. List the ordered pairs in the equivalents: reletien :12 en A with equivalence classes precisely the elements if: B. FPEIVE. ‘1‘ L'I'f‘ 4.) (6 pts.) If fenetien _,r‘ : A I—i B is ene—te—ene end fenetien g : B —e- C." is ﬁne-te—Zene, then feeetien gr: I : s1 —i G is ene-te-ene. 5.} {? pie.) Use the Principle of Methemetieel Induetien {Phil} te prove that l 1 l 1 n _ __ _ = EN. 3415+35+' +4n3—l se+1 v” 6.] [B 111.55.] Let fﬁm] = 4— 2 and ﬁx] = iii-1' be deﬁned fer all neimisenble real numbers. 3.] Find [9 e ﬂlfﬂm b.) What is the Derm[5ref}l 'i' e.) What is the Item 0 Jr] i T.) {'3' pts. eeeh} Use the Well-Ordering Prineiple [WGP] te pretre that every integer n 3 2 hes a prime teeter. I.) [E pts.} Let R be any reletien en set 31 and deﬁne IfR={yEA::I.-Ry} ..... end..." AIR={3,I"R:EEA} . Let A = {1,2,3} and let B = {{1,2]-, {3}}. Find twe distinct relations 12 and 1?. se that AIR = Aft} = 5‘, er sheer that this is meeesihle. 9.} ['Fpts.) Letﬁmetiensfzﬂ—iﬁendgzﬂ-ﬁﬂ. Preeethetifgoj;A—sﬂis ente C, then 913 —i f} is ente G. ' ...
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