![3. (6 marks) The idea of a sublanguage is exactly the same as the idea of a subset. L1 is a sublanguage of L2 if and only if all strings in L1 are also in L For example, if L1 {ab, abab) and L2 Ha, b, ab, ba, abab, abbaab), then L1 is a sublanguage of L2, and we write L1 SL2. For each of the statements below, prove that the statement is false by providing a counterex ample. [Hint: Think about the languages we have discussed in class as being non-regular.] (a) For all languages A and B, if ACB and B is non-regular, then A must be non-regular. (b) For all languages A and B, if A CB and Bis regular, then A must be regular.](http://img.homeworklib.com/questions/fdaac300-0d41-11ec-8fb8-d53aa4a747c3.png?x-oss-process=image/resize,w_560)
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The idea of a sublanguage is exactly the same as the idea of a subset. L_1...
3) Construct a regular expression defining each of the following languages over the alphabet {a, b}....
3) Construct a regular expression defining each of the following languages over the alphabet {a, b}. (a) L = {aab, ba, bb, baab}; (b) The language of all strings containing exactly two b's. (c) The language of all strings containing at least one a and at least one b. (d) The language of all strings that do not end with ba. (e) The language of all strings that do not containing the substring bb. (f) The language of all strings...
If L1 and L2 are Regular Languages, then L1 ∪ L2 is a CFL. Group of answer choices...
If L1 and L2 are Regular Languages, then L1 ∪ L2 is a CFL. Group of answer choices True False Flag this Question Question 61 pts If L1 and L2 are CFLs, then L1 ∩ L2 and L1 ∪ L2 are CFLs. Group of answer choices True False Flag this Question Question 71 pts The regular expression ((ac*)a*)* = ((aa*)c*)*. Group of answer choices True False Flag this Question Question 81 pts Some context free languages are regular. Group of answer choices True...
For each of the following statements, either prove the statement or give a counterexample that shows...
For each of the following statements, either prove the statement or give a counterexample that shows the statement is false. We will use the (non-standard) notation I to represent the irrational numbers Each problem is worth 10 points. 1. For all mEN2, m2-1 is composite. 2. For all integers a and b If ab is even then a is even or b is even. 3. For all integers a, b, and c If ale and ble then ablc
UueSLIORS! 1. Find the error in logic in the following statement: We know that a b'...
UueSLIORS! 1. Find the error in logic in the following statement: We know that a b' is a context-free, not regular language. The class of context-free languages are not closed under complement, so its complement is not context free. But we know that its complement is context-free. 2. We have proved that the regular languages are closed under string reversal. Prove here that the context-free languages are closed under string reversal. 3. Part 1: Find an NFA with 3 states...
5. (1 point) Which of the following statements is true? A. Recognizable languages are a subset...
5. (1 point) Which of the following statements is true? A. Recognizable languages are a subset of the decidable languages. B. Some decidable languages may not be recognizable. C. A decider for a language must accept every input. D. A recognizer for a language doesn't halt. E. A decider halts on every input by either going to an accept state or a reject state. 6. (1 point) Which of the following could be false for the language L = {abclixj...
Let A be a subset of R. If x € R we say x is a...
Let A be a subset of R. If x € R we say x is a boundary point of A if for all € > 0, (0 – €,x +E) NA # and (x - €, x+) NĀ+). The boundary of A is a A. It is the set of all boundary points of A. The interior of A is int A = A (BA). The closure of A is cl A = AU (DA). Let B be a subset...
Please Answer Question#02 Solution of Question 1 is attached. Solution of Questions #01 Please do Questions...
Please Answer Question#02 Solution of Question 1 is
attached.
Solution of Questions #01
Please do Questions #01 As soon as
possible.
= {a, b} will be used for all of the following exercises. The alphabet 1. Give regular expressions which exactly define the following languages. [7 marks] (a) L1 which has exactly one b but any number of as. (b) L2 which has an even number of as and an even number of bs. [7 marks] (c) L3 which contains...
1. Consider the alphabet {a,b,c}. Construct a finite automaton that accepts the language described by the...
1. Consider the alphabet {a,b,c}. Construct a finite automaton that accepts the language described by the following regular expression. 6* (ab U bc)(aa)* ccb* Which of the following strings are in the language: bccc, babbcaacc, cbcaaaaccbb, and bbbbaaaaccccbbb (Give reasons for why the string are or are not in the language). 2. Let G be a context free grammar in Chomsky normal form. Let w be a string produced by that grammar with W = n 1. Prove that the...
PLEASE, ANSWER ALL SUBPARTS AND ALL THE EXERCISES!! DO NOT DO JUST ONE. ALSO, SHOW COMPLETE...
PLEASE, ANSWER ALL SUBPARTS AND ALL THE EXERCISES!! DO
NOT DO JUST ONE. ALSO, SHOW COMPLETE STEPS. THANK YOU!
1. Find the determinant of each of the matrices below using (1) row operations-transforming each matrix to an upper-triangular form or (2) cofactor expansion. (a) A = ſi 1 1 1 2 2 2 3 (b) A= ſi 2 3 2 2 3 0 3 0 1 (c) A [1 0 0 1 0 1 1 1 0 1 1 0...
3. (12 pt) Suppose that S is the subset of R2 that contains all vectors on...
3. (12 pt) Suppose that S is the subset of R2 that contains all vectors on the two lines y = x and y = -2 s={[x] € R: y=x or y = -x} ER2: y = r or y=- (a) In each of the following parts (i)-(iii), either show the statements is true or give a counterexample to show that the statement is false. Clearly state TRUE or FALSE. Graphs of y = x and y = -1 may...
For each of the following statements, either prove the statement or give a counterexample that shows the statement is false. We will use the (non-standard) notation I to represent the irrational numbers Each problem is worth 10 points. 1. For all mEN2, m2-1 is composite. 2. For all integers a and b If ab is even then a is even or b is even. 3. For all integers a, b, and c If ale and ble then ablc
UueSLIORS! 1. Find the error in logic in the following statement: We know that a b' is a context-free, not regular language. The class of context-free languages are not closed under complement, so its complement is not context free. But we know that its complement is context-free. 2. We have proved that the regular languages are closed under string reversal. Prove here that the context-free languages are closed under string reversal. 3. Part 1: Find an NFA with 3 states...
5. (1 point) Which of the following statements is true? A. Recognizable languages are a subset of the decidable languages. B. Some decidable languages may not be recognizable. C. A decider for a language must accept every input. D. A recognizer for a language doesn't halt. E. A decider halts on every input by either going to an accept state or a reject state. 6. (1 point) Which of the following could be false for the language L = {abclixj...
Let A be a subset of R. If x € R we say x is a boundary point of A if for all € > 0, (0 – €,x +E) NA # and (x - €, x+) NĀ+). The boundary of A is a A. It is the set of all boundary points of A. The interior of A is int A = A (BA). The closure of A is cl A = AU (DA). Let B be a subset...
Please Answer Question#02 Solution of Question 1 is
attached.
Solution of Questions #01
Please do Questions #01 As soon as
possible.
= {a, b} will be used for all of the following exercises. The alphabet 1. Give regular expressions which exactly define the following languages. [7 marks] (a) L1 which has exactly one b but any number of as. (b) L2 which has an even number of as and an even number of bs. [7 marks] (c) L3 which contains...
1. Consider the alphabet {a,b,c}. Construct a finite automaton that accepts the language described by the following regular expression. 6* (ab U bc)(aa)* ccb* Which of the following strings are in the language: bccc, babbcaacc, cbcaaaaccbb, and bbbbaaaaccccbbb (Give reasons for why the string are or are not in the language). 2. Let G be a context free grammar in Chomsky normal form. Let w be a string produced by that grammar with W = n 1. Prove that the...
PLEASE, ANSWER ALL SUBPARTS AND ALL THE EXERCISES!! DO
NOT DO JUST ONE. ALSO, SHOW COMPLETE STEPS. THANK YOU!
1. Find the determinant of each of the matrices below using (1) row operations-transforming each matrix to an upper-triangular form or (2) cofactor expansion. (a) A = ſi 1 1 1 2 2 2 3 (b) A= ſi 2 3 2 2 3 0 3 0 1 (c) A [1 0 0 1 0 1 1 1 0 1 1 0...
3. (12 pt) Suppose that S is the subset of R2 that contains all vectors on the two lines y = x and y = -2 s={[x] € R: y=x or y = -x} ER2: y = r or y=- (a) In each of the following parts (i)-(iii), either show the statements is true or give a counterexample to show that the statement is false. Clearly state TRUE or FALSE. Graphs of y = x and y = -1 may...
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