Regular Expressions are an algebraic way to describe languages.
Regular Expressions describe exactly the regular languages.
If E is a regular expression, then L(E) is the regular language it defines.
For each regular expression E, we can create a DFA A such that L(E) = L(A).
A regular expression regexp followed by * matches a string of zero or more strings that matches regexp.
For example, A* matches A , AA , AAA and so forth.
It also matches the null string (zero occurrences of A ). ).
A regular expression regexp followed by + matches a string of one or more strings that matches regexp.
In general ( a + b )k corresponds to the set of strings of length k over the alphabet {a, b}. ( a + b )* corresponds to the set of all strings over the alphabet {a, b}. a*b* corresponds to the set of strings consisting of zero or more a's followed by zero or more b's.
Answer and Explanation:
Then, (-2a-12), The equivalent expression -2(a+6), Hence, The correct option is c.
What are equivalent expressions? Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s). khanacademy.org
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s). [Examples] khanacademy.org
•Distributing coefficients and combining like terms in algebraic expressions •Recognizing equivalent algebraic expressions •Solving for an unknown coefficient using two equivalent expressions •Rearranging formulas containing 2 or more variables khanacademy.org
Questions about equivalent expressions usually feature both and . To check which complex expression is equivalent to the simple expression: 1.Distribute any coefficients: a(bx±c)=abx±ac . 2.Combine any like terms on each side of the equation: x -terms with x -terms and constants with constants. 3.Arrange the terms in the same order, usually x -term before constants. khanacademy.org
Some questions will present us with an equation with algebraic expressions on both sides. On one side, there will be an unknown coeffient, and the question will ask us to find its value. For the equation to be true for all values of the variable, the two expressions on each side of the equation must be equivalent. For example, if ax+b=cx+d for all values of x , then: •a must equal c . •b must equal d . To find the value of unknown coefficients: 1.Distribute any coefficients on each side of the equation. khanacademy.org
Formulas are equations that contain 2 or more variables; they describe relationships and help us solve problems in geometry, physics, etc. Since a formula contains multiple variables, sometimes we're interested in writing a specific variable in terms of the others. For example, the formula for the area, A , for a rectangle with length l and width w is A=lw . It's easy to calculate A using the formula if we know l and w . However, if we know A and w and want to calculate l , the formula that best helps us with that is an equation in which l is in terms of A and w , or l=Aw . Just as we can add, subtract, multiply, and divide constants, we can do so with variables. To isolate a specific variable, perform the same operations on both sides of the equation until the variable is isolated. The new equation is equivalent to the original equation. [Example] khanacademy.org
TRY: IDENTIFYING EQUIVALENT EXPRESSIONS Which of the following expressions is equivalent to 4x−3 for all values of x ? Choose 1 answer: Choose 1 answer: •(Choice A) 2(2x−3) khanacademy.org
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable. To check whether a more complex expression is equivalent to a simpler expression: 1.Distribute any coefficients: a(bx±c)=abx±ac 2.Combine any like terms on each side of the equation: x -terms with x -terms and constants with constants 3.Arrange the terms in the same order, usually x -term before constants. 4.If all of the terms in the two expressions are identical, then the two expressions are equivalent. khanacademy.org
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A+ A A- B+ B B- C+ C C- D+ D E
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Notation française. Notation. Américaine. (6ème à la 3ème) (2nde à la terminale). A+. 16-20. 15-20. A. 15. 14. A-. 14. 13. B+. 13. 12. B. 12. 11. B-. |
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A. Base erosion and profit shifting using interest and payments economically equivalent to interest ..... 6. B. The BEPS project and interest expense . |
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EU. 65 AA. 65 A. 65 B. 65 C. 65 D. 65 E. 65 F. 65 G. 65 H. 65 J. 70 AA. 70 A. 70 B. 70 C. 70 D. 70 E. 70 F. 70 G. 70 H. 70 J. FR. 80 AA. 80 A. 80 B. |
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B-/C. 4-4.99. 50-62.99. Austria. US GPA. US Letter grade. Austrian scale. 3.5-4.0. A. 1-1.99. 3.3-3.49. B+. 2-2.99. 2.99-3.29. B. 3-3.99. Below 3.0. B-/C. |
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Regular Expressions
Thus, ab + c is equivalent to (ab) + c, not to a(b + c), which would denote a different language: {ab, ac} The only way to define an infinite language using regular |
Regular Expressions
The expressions (ab) ∗ represents the language {ϵ, ab, abab, ababab, } The expression (a + b) ∗ represents the words built only with a and b The |
Regular Languages and Finite Automata-II - Department of
9 déc 2020 · Find a DFA to recognize (a + ba)*bb(a + ab)* DFA and NFA are equivalent concept example are equal, i e , a*a( ba* a)* = (a + ab)*a |
Exercises
(iii) (ba*a + ab*b)*ab* (iv) (ba*a + aa*b) *aa* (v) (ba*a + ba*b)*ba* a 14 Give an NFA with four states equivalent to the regular expression (01 + 011 + 0111)* |
Homework 3 Solutions
i e , C = L(M) Since every NFA has an equivalent DFA (Theorem 1 39), there Thus, the NFA can't go anywhere from states 2 and 3 on a b, so we add a b-edge |
Homework 4
described in Lemma 1 60 to convert the following DFA M to a regular expression 1 2 3 a, b a b b a Answer: First convert DFA M into an equivalent GNFA G 2 |
Written Assignment 1 Solutions
1 Write regular expressions for the following languages over the alphabet Σ = {a, b}: (a) All strings that do not end with aa ϵ + a + b + (a + b) ∗ (ab + ba + bb) |
10 - Languages, Regular Expressions, Finite Automata
ab + ba matched by exactly two strings: ab and ba b* matched by { λ, b, bb, a b , so don't try to use "algebra” 2 ex: (a+b) = (a+b)(a+b) = aa or ab or ba or bb |
(a) all strings containing exactly one a
2 Find a regular grammar that generates the language L(aa*(ab + a)*) Solution G |
CS 341 Homework 3 Languages and Regular Expressions 1
(b) Any string of a's and/or b's with at least one occurrence of ab or ba We can prove that two sets X and Y are equal by showing that any string in X must also |
[PDF] Regular Expressions
The expressions (ab) ∗ represents the language {ϵ, ab, abab, ababab, } The expression (a + b) ∗ represents the words built only with a and b The |
[PDF] Homework 3 Solutions
ie, C = L(M) Since every NFA has an equivalent DFA (Theorem 139), there Thus, the NFA can't go anywhere from states 2 and 3 on a b, so we add a b edge |
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Jan 4, 2016 · Bioequivalence refers to equivalent release of the same drug substance from two or more drug products or formulations These two definitions |
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Why are we assuming that the number of columns of A is equal to the number of rows of B? Proof 2 Assumptions AB = BA Need to show A and B are both square |
[PDF] CS 341 Homework 3 Languages and Regular Expressions 1
So (b*ab*ab*a)*b* Since the first expression has * around it, it can occur 0 or more times, to give us any number of a's that is divisible by 3 (b) Another way to |
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Reflexivity (a, b) ∼ (a, b) if ab = ba, which is true since multiplication in Z is We usually interpret these pairs of numbers as equivalent, or “equal” fractions |
[PDF] AB if A then B if not B then not ATTTTTFFFFTTTFFTT
table are said to be equivalent The table shows that a conditional and it's contrapositive are equivalent A conditional is vacuously true if its antecedent is false |
Source: Alexandros Antonatos - Academiaedu
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