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3. Consider these 2 statements:
S1: LR = L, if and only if L is the language of palindromes.
where LR is obtained by reversing all the strings of L.
S2: | L1∙ L2 | = | L1 | × | L2 |
Relation?
(a) Both are F (b) Both are T
(c) S1 → T, S2 → F (d) S1 → F, S2 → T
asked in Theory of Computation by Active (2.8k points) | 55 views

2 Answers

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For Statement 1:-

you know that w=wR ===>  it is a palindrome string.

let L= Collection of Strings  which are palindromes ===> LR = reversing each string in L = string in L

∴ S1 is TRUE.

 

For Statement 2 :-

| L1.L| = |L1| X | L2 |

LHS = concatenate L1 string, L2 String and take the length of resultant

RHS = Take the length of string in L1, length of string in L2 and multiply them 

Obvisiouly it is a relation....but not a function, 

answered by Boss (42.2k points)
edited by
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please explain the 2nd statement by taking two languages
0

take L1 = {0,01,10,111}, L2={1010,1011,10101}

| L1 . L2 | = | {0,01,10,111} . {1010,1011,10101}  | ===> have 12 elements

 

0 . 1010 ===> | L1 . L2 | = 5 , | L1 | X | L2 | = 5

0 . 1011 ===> | L1 . L2 | = 5 , | L1 | X | L2 | = 5

0 . 10101  ===> | L1 . L2 | = 6 , | L1 | X | L2 | = 5

01 . 1010  ===> | L1 . L2 | = 6 , | L1 | X | L2 | = 8

01 . 1011  ===> | L1 . L2 | = 6 , | L1 | X | L2 | = 8

01 . 10101  ===> | L1 . L2 | = 7 , | L1 | X | L2 | = 10

10 . 1010  ===> | L1 . L2 | = 6 , | L1 | X | L2 | = 8

10 . 1011  ===> | L1 . L2 | = 6 , | L1 | X | L2 | = 10

10 . 10101  ===> | L1 . L2 | = 7 , | L1 | X | L2 | = 10

111 . 1010  ===> | L1 . L2 | = 7 , | L1 | X | L2 | = 12

111 . 1011  ===> | L1 . L2 | = 7 , | L1 | X | L2 | = 12

111 . 10101  ===> | L1 . L2 | = 8 , | L1 | X | L2 | = 15

 

the relation look like as {(5,5), (6,5), (6,8), (6,10), (7,10) , (7,12), (8,15) }  but it is not a function

sorry for that, i will edit my answer.

0
thanks
0

is ans given as c?

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yes
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according to answer i hope

Then they meant to ask Statement 2 is a Function why because there is no meaning asking is it a relation or not?
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What is the answer given?
answered by Active (1.8k points)
0
option c
0
Okay.

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