regular expressions

Question

Consider the following statements, which comprises the equality between some regular expressions:

S1: ε. ф*= ε. ф+

S2: ф. ф* = ф .ф+

Select the correct option.

 

1. Both S1 and S2 are correct.

 

2. Both S1 and S2 are false.

 

      3.S1 is false while S2 is correct.

 

4. S1 is correct while S2 is fals

Comments

S1: ε. ф*= ε. ф+

S2: ф. ф* = ф .ф+

For S1:

we can write  ф+ = ф.ф*  And ф* = ε

ε.ε    = ε.ф+

ε = ε.ф.ф*  ===>  ε   = ф   ====>>> ε    != ф ( False)

For S2:

ф. ф* = ф .ф+  ====>> ф.ε   = ф.ф.ф*   ====> ф  = ф ( True)

 

Option C is correct.

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what does ф , ф+ and ф*  denotes ?

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@Satbir

ф means empty language,ε is empty string

ф*=ε

ф+= фф*=ф.ε=ф

Answer 1

c