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2. Prove the following using the properties of regular expressions: (ab)* +c+c=A+ ab +(ab)" + c(A+c") 3. Prove the following using the properties of regular expressions: (ab)-(c+d) = (ab)(c +c)+(ab)-(A+d)

2. Prove the following using the properties of regular expressions: (ab)* +c+c=A+ ab +(ab)" + c(A+c") 3. Prove the following using the properties of regular expressions: (ab)-(c+d) = (ab)(c +c)+(ab)-(A+d)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Book problem 5 all parts (page 747) Be sure to show your work for these (and all problems!) Simplify each of the following regular expressions. a. A+ ab + abab(ab)" b. aa(b + a) + a(ab- + aa) c. a(a + b) + aa(a + b)* + aaa(a + b)- 2. Prove the following using the properties of regular expressions: Properties of Regular Expression Name we will use in proofs: R+T-T+R plus 1.1 R+O=D+R=Rplus 1.2 R+R-A. plus 1.3 (R+S) T-R+18+7) plus 1.4 Re-R-. do 2.1 RA-AR-it dot 2.2 (RA)T-R(ST) det2.3 & (Derilerine properties) RER+7)=RRY, distrib3.1 (8 + 7)R-SR 78 db32 4-A²-A dosure 4.1 5. N-X-(""-R-R closure 5.1 X² - A+ X² − (X + 2-12-2³ "-". closure 6 3. Prove the following using the properties of regular expressions: (+) A+, dosure 52 21.closure 53 21. closure 54 T. (+5)-(+5-5-5-5"closure 7 MAR-SY&cure 8 SA++ SS. closure 9.1 RS-A+R(+5) dosure 9.2 (ab)* +c+c=A+ ab +(ab)* + c(A+c") (11.1) (ab)-(c + d) = (ab)-(c+c)+(ab)-(A+a)
Transcribed Image Text:1. Book problem 5 all parts (page 747) Be sure to show your work for these (and all problems!) Simplify each of the following regular expressions. a. A+ ab + abab(ab)" b. aa(b + a) + a(ab- + aa) c. a(a + b) + aa(a + b)* + aaa(a + b)- 2. Prove the following using the properties of regular expressions: Properties of Regular Expression Name we will use in proofs: R+T-T+R plus 1.1 R+O=D+R=Rplus 1.2 R+R-A. plus 1.3 (R+S) T-R+18+7) plus 1.4 Re-R-. do 2.1 RA-AR-it dot 2.2 (RA)T-R(ST) det2.3 & (Derilerine properties) RER+7)=RRY, distrib3.1 (8 + 7)R-SR 78 db32 4-A²-A dosure 4.1 5. N-X-(""-R-R closure 5.1 X² - A+ X² − (X + 2-12-2³ "-". closure 6 3. Prove the following using the properties of regular expressions: (+) A+, dosure 52 21.closure 53 21. closure 54 T. (+5)-(+5-5-5-5"closure 7 MAR-SY&cure 8 SA++ SS. closure 9.1 RS-A+R(+5) dosure 9.2 (ab)* +c+c=A+ ab +(ab)* + c(A+c") (11.1) (ab)-(c + d) = (ab)-(c+c)+(ab)-(A+a)
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