MTH 207 Exam 2 Sample, Spring 2016

Discrete Structures I Exam 2 make up (May 9, 2012) 1, Let A = {1, {1}, {1,2}, ¢, {¢}} . Answer the following by True or False: (a) {1}e A \ — ] (b) 6c A \ ay « (c) gre A 7 VY. —— @) {4eHca F () {2HCA AT (f) {L2,{}} cA ia @) {(@}cA —T 2. Give an example of a function f : Z— Z that is 1-1 but not onto. tol of C*) = oon et 3. Show in details that if f : A B and g: B — C are both onto, then so is fey: A> C . ap ee Fad 2 eh sh Aye) =< LfG)s=< Gm - ve oe q & eB IJ sh, renee for we 4 acy sk. ta) = bo A (> e 5 C A a [4¢) |~< on yk Care si: ents ‘ (a) Is f 1-1? (oy, tof. io. 4. Let f:Zx Z— Z be defined by f(m,n)=m? +n Po { (2%) = £(-%)) = 5 £m t -(. ee 5. For which numbers 2 and y is it true that [z+ y] = [a] + |yJ?E xplain . Ay dlr anol { xnVe @ Wee ogy Cet - nad whos. ne Leh T as Nt » Siac n= Ls > ye reed ocdald | \,0y3 1,2,3 6. Under what conditions is AUB = AU(B-— A)? “Pp 7. If f: A B be 1-1. Show that f(SUT) = f(S)U f(T), where S and T are subsets of A. lof. Dobe tm Seeston + 4 — _ . a wAsre. ew ge6leee HO, ne SOT SS oe £65) VET) Lge bl) OOD) 2B, EOD TL 7” 2 whos Aaé a ° 0 = esi. 82 7 6 ok: We de home Qe eR 8. Show whether or not f = O(f * 9) awe. tof et Be 09 7a a ed Le wh a ° £° O/ #2) 100 9. Evaluate in an efficient way (3? + 5¢+ 4) leo i=4 (eo loo 2 . 2 =. ; 527 + = & lo/ ° ic& © ee beg = - 3 t iz “jal i hye i ) Y MS “ME | Sue _ sfoseaes - +a "Fae a us 10. Show that ifz ¢€R, thenz-1<([z|<2< It]<e+l lof fe 2 Ned o<d <I