(a+b)* is equivalent to
Which type of language is represented by regular expression?
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.
What does a B )* mean?
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.
Which expression is equivalent to (- 2 )( a 6?
Answer and Explanation:
Then, (-2a-12), The equivalent expression -2(a+6), Hence, The correct option is c.
Overview
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
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). [Examples] khanacademy.org
What skills are tested?
•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
How do we recognize equivalent expressions?
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
How do we solve for unknown coefficients?
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
How do we rearrange formulas?
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
Your turn
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
Things to remember
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
Centre d'études du religieux contemporain. Sherbrooke (Québec) J1K 2R1. (819) 821-7600 (téléphone). (819) 821-7677 (télécopieur). SYSTÈME DE NOTATION. |
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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 |
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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)* |
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Homework 3 Solutions
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Homework 4
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Written Assignment 1 Solutions
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