Regular languages?

Question

Comments

La = a^x where x is even  => Regular

Lb = a^x*b^y, Language is finite => Regular

Lc = {a}, generates only one string => Regular

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Can you explain 1st one plz

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La = a^x*a^y and since x=y

=> La = a^x* a^x

=> La = a^2x

=> La = a^m where m = 2x. which means generating even no. of as

Answer 1

L_b and L_c is regular
Reason for L_b is that it requires no of ways to factor 4096 and that's finite for sure

Coming to L_c, the line of reasoning is that it doesn't require any counting or comparisons, so it is finite although integral solutions to x-y=19 are infinite