Test by Bikram | Mock GATE | Test 1 | Question: 50

Question

Consider the regular languages denoted by the following pairs of regular expressions:

1. $(0 + 1)$*$ = 0$*$ + 1$*$ $
2. $0(120)$*$12 = 01(201)$*$2$
3. $(0$*$l $*$)$*$ = (0$*$1)$*$ $
4. $(01 +0)$*$0 = 0(10 +0)$*$ $ 

Determine the truth of equality for each pair.

1. $a-False, b-True, c-True, d-False$
2. $a-True, b-False, c-False, d-True$
3. $a-True, b-True, c-False, d-True$
4. $a-False, b-True, c-False, d-True$

Answer 1

Answer is (D)
Explanation:

a) (0+1)* = 0*+1* (LHS is syring containing 0s and 1s while RHS is string containing either 0s or 1s but both both for eg 00100, 010,011, etc are anti-examples) False

b) 0(120)*12 = 01(201)*2  (You can pass any string) True

c) (0*1*)* = (0*1)*  

Here, LHS=Any string while RHS=Ends with 1 (you can's pass strings like 100,00,1100,etc. False

d) (01 +0)*0 = 0(10 +0)*  Both strings starts and Ends with '0' and NO 1's together(alternative 1's) True

So, answer is FTFT which is in option (D)

Correct me if I'm wrong!

Comments

Thanks brother,,,Doing great Job, most OPTIMAL TEST SERIES  i can say,,

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Ok, so I was wrong I did that silly mistake which I shouldn't do! Updating my answer

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b. 0(120)*12 = 01(201)*2 is False.
Example String: 012012012. This string can be generated using the 01(201)*2 but cannot be generated with 0(120)*12. Check for yourself if you want.
Hence, correct option should be FFFT. not in any of the options