Question

Given the following language definition: L = {w ϵ {a, b}* : x ϵ {a, b}+ (w = axa)} ||| Give a simple English description, two words it contains, and two it does not.

Answer 1

The words must all begin with 'a' and end with 'a'

Answer 2

can there be a string with zero length?

Answer 3

no

Answer 4

is this because of the plus sign?

Answer 5

but i don't understand fully what you are trying to say.

Answer 6

basically looking for strings which would be found in the language as defined in the question

Answer 7

\[ L = \{ w \in (a,b)^*:x\in (a,b) + (w=a \times a) \}\]
how do you interpret this statement?

Answer 8

There is a language such that w is an element of L containing any combinations of the symbols 'a' and 'b'...

Answer 9

If X is in L, and contains at least one a and b, X must begin with a and end with a

Answer 10

this last part means that there cannot be a string with no b's unless if is an empty string

Answer 11

I have never seen those representation before. I think there is no word in English that begins with 'a' and ends with 'a' and only containing 'a' and 'b'. If a set does not have any elements then it's a null set.

Answer 12

try searching for few words online
http://www.thefreedictionary.com/

Answer 13

English has nothing to do with it, except that I need to explain the fictional language in English

Answer 14

isn't this related to sets??

Answer 15

yes, the words which make up the language will be a set of words, the first being the empty set

Answer 16

sorry, word with no characters, not the empty set

Answer 17

then you can have infinite words. begin with 'a' then add up as much as you like, then again end with 'a'.

Answer 18

is there one exception, meaning the plus sign (one or more)?

Answer 19

x is an element of words with at least one a and one b if it begins with a and ends with a?

Answer 20

just get the two word that is contained in X and 2 word not contained in X.
eg. aba, ababa <--- these two are contained in X
eg. baba, abab <--- these two are not contained in X

Answer 21

L being superset of X, contains all those 4 elements, but X does not contain those last two elements of L, because of the criteria imposed on X for its members.

Answer 22

X appears to be a representation of a substring of strings which begin with a and end with a, not a subset of L

Answer 23

don't you need a word that X does not contain?

Answer 24

that L does not contain

Answer 25

a word that is contain in X but not contain in L?

Answer 26

X is merely a representation of a word within L it appears

Answer 27

so you need 2 words that L does not contain?

Answer 28

yes

Answer 29

any word containing 'a' and 'b' would be contained in L, either we construct a word from other characters or there is no such word.

Answer 30

bab would be a word not in L?