Plz explain

Question

. 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 2 (c) S1 → T, S2 → F (d) S1 → F, S2 → T

Answer 1

For S1: Take L = { ab, ba }
For S2: Take L1 = { a, aa }, L2 = { ab, b }

Comments

Can you elaborate and explain your answer. I saw the answer as (c) S1→T, S2→F in one mock test.
How is S1 true?

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if L1={a,aa} and L2={ab,b}
then L1.L2={aab,ab,aaab,aab}
and L1xL2={aab,ab,aaab,aab}
so |L1.L2| = |L1xL2| both are equal.
@srestha please varify this

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yes , that is correct.

but here asking | L1∙ L2 | = | L1 | × | L2 |

where |x|= length of language x.

if L1={a,aa,b} and L2={ab,b}
then L1.L2={aab,ab,aaab,aab,bab,bb} ={aab,ab,aaab,bab,bb} as aab coming duplicate

|L1.L2|=5

Now

|L1|.|L2|=3.2=6

Both cases not same

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How do you define x and "." in the question? Otherwise, how do you answer this? @Reena To prove something false, just one counterexample is enough. But to prove something true we should show that no counterexample exists.