CS 321 Assignment 1
docx
keyboard_arrow_up
School
Portland Community College *
*We aren’t endorsed by this school
Course
464
Subject
Mathematics
Date
Nov 24, 2024
Type
docx
Pages
3
Uploaded by ProfessorIceCat10
Section 1.1: /") SecHon 1.5 ) To pvove [25|=2"%1 weli use EUNciple of aihematcal induckon. Lerle suppose S is an emety set+hen‘|s|:‘o. 2= rep(eéén'f's> fhe cardinality of power set S-Hhat have only single element, Le. | epty set (125)=1) 21812 9% Lecauce 1€l= 0. So 2% 4 Base case holds for [25]= 2", Tnductive Hupothesis - Let's suppose that k. fs some, positive infeqertnen 125[=2*" holds when (=K. Induchie Step: | - T s skep, well prove Haf ie [S1= kL +hen [251=2". E Let S (s a fintte set with IS|=k+2, We can write i+ as+he unfon of two digjoirtt sers> S=5a% LB, whee $at is a set containing only one dement & and. B s a set having cardinality k., Ce. Bl =K. Now, ) A= Zf(ia.} UR)% 2F = 7_{““3)3 o 228 - By using property of powex set 28| = |2?.65.4§)>U 218} | 2% =| 22(3.0&53\ + ]233’5\ ~. Cardinality of union is sum of cardinalities. - QUELAI, l"] PRI 2% Q.fi'Bu 23] = S By inductve hypothesis sz ® lence,we have proved that (¢ [$]= K+ [, then 125/ =2 holds. A e —
Section 1.2: - | 2) e languade genexated by +his grammar contains Hie sHings having only a's. Morzever; the nuniber of als generated by +his grammar sheuld be the wulkiple of 2/s Hhat is (dd,4aa4,44424a,.,,). So we can ey that Hhe [anguage generdted by given gaammar showld have even, nwumber of a's exeluding null. irl _ | l 1 | i ! il ‘ ‘Inllilll‘,llli Section 2.1: 3. || JFLAP : (DFA3 jff) File Input Test View Convert Help ¢ Table Text Size [ ) Input Result Reject b Accept aa Reject aab Accept aabb Reject aabbb Accept aba Accept baa Accept bbab Reject bbaba Accept baabb Accept
4. [£] JFLAP : (DFA4,jfF) File Input Test View Convert Help Table Text Size Input Result aaa Reject aabbbbab Reject : Accept ‘|aaaabbbbb Reject :|abababa Accept :\bababa Accept aabbaabb Accept |£| JFLAP : (DFAS.jff) X File Input Test View Convert Help E Table Text Size [ ) Input Result Accept a Accept aa Accept aaa Reject 3aaa Accept a3aaaa Accept 3aaaaa Reject
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help