Simplify the following expressions 1. А[В + С (АВ + АС)] 2. А + B[AC + (В + C)DI 3. (А + (ВС)У (AВ' + АВC)
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![Simplify the following expressions
1. А[В + C (АВ + АC)]
2. А + B[AC + (В + C)DI
3. (А + (ВC)) (АВ' + АВC)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F303edd4e-4360-4570-907a-6f8de3840bf5%2F86c892b0-cf6c-4d66-b0ae-6cf7fe9883b7%2Fiqtmb3m_processed.png&w=3840&q=75)
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- Syntactically different regular expressions may represent the same language. Consider regularexpressions over Σ = {0, 1}. Which of the following equations hold? (You don’t need to justifyyour answers.) 1. ε + 0 = ε + ε + 02. ε + 0∗ = 0∗3. (00 + 10)∗ = (01 + 11)∗4. 0 + ∅ = 0Simplify the following grammar. S→ aAa A → bBB | D B → ab | E C → aBComputer Science Suppose L ⊆{a, b}∗ is defined as follows: Λ∈L; for every x and y in L, the strings axb, bxa, and x yare in L. Show that L =AEqB , the language of all strings x in {a, b}∗ satisfying n_a (x) =n_b (x).
- Please translate the following English sentence into a sentence of FOL: use quantifiers "Lucia owns exactly one guitar" Domain: people and things M(x): x is a musician G(x):x is a guitar player R(x): x is a guitar O(x,y): x owns y L: luciaFor each of the following languages, give two strings that are members and two strings that are not members—a total of four strings for each part. assume Σ = {a,b} in all parts A. a*b* B. a(ba)*b C. a* U b* D. (aaa)* E. Σ*a Σ*b Σ*a Σ* F. Aba U bab G. (Є U a)b H. (a U ba U bb) ΣThe language of the following DFA is { w∈{0,1)* | _________ } a) w ends in a 0 b) w contains a 1 c) w has an odd number of 1’s d) w starts and ends with a 0 and has a 1 e) w contains a 1 and ends in a 0
- Label the following statement as True (T) or False (F): The following context-free grammar is in Chomsky normal form: S → XY | XZ X → XX | XY | aa Y → YY | b Z → ZX | ε2- Write a regular expression for each of the following languages over {a,b}: • String of a's and b's that begin with a and end with b. • Strings that have at least two a's. • Strings that have an even number of a's. • Strings that do not have two a's in a row. • Strings that do not end with the substring ab.Write regular expressions for the following languages on {0, 1}. A. all strings ending in 10, B. all strings not ending in 10,
- For the following pairs of expressions, find a unifier for each pair if a unifier exists. If a unifierdoes not exist, explain why.(a) p(X,Y) and p(a,Z)(b) p(X,X) and p(a,b)(c) f(X,Y) and f(a,g(a))(d) q(X) and ¬q(a)ASAP NLP!! Write regular expressions for the following languages. The set of all alphabetic strings end with a;Not handwritten Find dfa's that accept the following languages. (c) L ((abab)* + (aaa* + b)*).