if L1, and L2 are subsets of {a, b}* then L U L (L,U L2)*. Show that LUL # (L1UL2)*.

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if L1, and L2 are subsets of {a, b}* then L U L (L,U L2)*. Show that
LUL # (L1UL2)*.
Transcribed Image Text:if L1, and L2 are subsets of {a, b}* then L U L (L,U L2)*. Show that LUL # (L1UL2)*.
Finite language is a language with finite number of strings in it, i.e., there exist exactly k strings in this
language such that k eNand k #00. For a finite language L, let |L| denote the number of elements of
L. For example, |{A, a, ababb}| = 3. (Do not mix up with the length |x| of a string x.) The statement
|L,L2| = |L1||L2| says that the number of strings in the concatenation LL2 is the same as the product
of the two numbers |L1| and |L2|. Is this always true? If so, prove, and if not, find two finite languages
L1, L2 S {a, b}* such that |L1L2| # |Li||L2l.
Transcribed Image Text:Finite language is a language with finite number of strings in it, i.e., there exist exactly k strings in this language such that k eNand k #00. For a finite language L, let |L| denote the number of elements of L. For example, |{A, a, ababb}| = 3. (Do not mix up with the length |x| of a string x.) The statement |L,L2| = |L1||L2| says that the number of strings in the concatenation LL2 is the same as the product of the two numbers |L1| and |L2|. Is this always true? If so, prove, and if not, find two finite languages L1, L2 S {a, b}* such that |L1L2| # |Li||L2l.
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