Identify the string set for the Σ {0,1} even count of zeros and odd count of onesa.{001,100,01,0000111,10101,0011}b.{0101,1010,1001,01000111,101001}c.{ε,001,100,0000111,101101}d.{111,001,100,0011100,0000111,10101}
Question
Identify the string set for the Σ {0,1} even count of zeros and odd count of onesa.{001,100,01,0000111,10101,0011}b.{0101,1010,1001,01000111,101001}c.{ε,001,100,0000111,101101}d.{111,001,100,0011100,0000111,10101}
Solution
The string set for the Σ {0,1} with an even count of zeros and an odd count of ones can be identified by counting the number of 0s and 1s in each string. The string set must have an even number of 0s and an odd number of 1s.
a. {001,100,01,0000111,10101,0011}
- 001: 2 zeros (even), 1 one (odd) - valid
- 100: 2 zeros (even), 1 one (odd) - valid
- 01: 1 zero (odd), 1 one (odd) - invalid
- 0000111: 4 zeros (even), 3 ones (odd) - valid
- 10101: 2 zeros (even), 3 ones (odd) - valid
- 0011: 2 zeros (even), 2 ones (even) - invalid
b. {0101,1010,1001,01000111,101001}
- 0101: 2 zeros (even), 2 ones (even) - invalid
- 1010: 2 zeros (even), 2 ones (even) - invalid
- 1001: 2 zeros (even), 2 ones (even) - invalid
- 01000111: 4 zeros (even), 3 ones (odd) - valid
- 101001: 2 zeros (even), 3 ones (odd) - valid
c. {ε,001,100,0000111,101101}
- ε: 0 zeros (even), 0 ones (even) - invalid
- 001: 2 zeros (even), 1 one (odd) - valid
- 100: 2 zeros (even), 1 one (odd) - valid
- 0000111: 4 zeros (even), 3 ones (odd) - valid
- 101101: 2 zeros (even), 4 ones (even) - invalid
d. {111,001,100,0011100,0000111,10101}
- 111: 0 zeros (even), 3 ones (odd) - valid
- 001: 2 zeros (even), 1 one (odd) - valid
- 100: 2 zeros (even), 1 one (odd) - valid
- 0011100: 4 zeros (even), 3 ones (odd) - valid
- 0000111: 4 zeros (even), 3 ones (odd) - valid
- 10101: 2 zeros (even), 3 ones (odd) - valid
So, the string sets that satisfy the condition are a, c, and d, but not b.
Similar Questions
how many number of states do we require for evaluating a string which has odd count of 0's odd count of 1's even count of 2'sa.14b.16c.4d.8
Which language accepted by the regular expression (0+1)*0(0+1)*0(0+1)*.Select one:a. The set of all strings containing at least two 0’s.b. The set of all strings that begin and end with either 0 or 1.c. The set of all strings containing at most two 0’s.d. The set of all strings containing the substring 00.
{ w | w∈ Σ {0,1} consists of an equal number of 0 and 1 }a.{0011,10,1001,001110}b.{0011,101,10101,001110}c.{0011,12,10101,001110}d.{0011,10,10101,001110}
The given automata will accept .........................a)even number of 0's and odd number of 1's.b)odd number of 0's and odd number of 1's.c)odd number of 0's and even number of 1's.d)even number of 0's and even number of 1's.
what is equivalent RE of the language: the set of strings of 0's that contains exactly 4 1's Question 1Select one:a.0*10*10*10*10*b.(0+1)*+(0+1)*1(0+1)*+(1*01*01*)c.((0+1)*10(0+1)*)+((0+1)*01(0+1)*)d.1*(01*01*01*)1*
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.