Question

Give regular expressions describing each of the following regular languages over Σ = {0,1}:

{w : w begins and ends with the same symbols}

show work!

Answer 1

Answer:
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(0(0+1)*0) + (1(0+1)*1)

Explanation:
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(0+1) matches exactly one 0 or 1
and, (0+1)* matches 0 or more 0's and 1's together
so, 0(0+1)*0 indicates binary strings beginning and ending with 0
and, 1(0+1)*1 indicates binary strings beginning and ending with 1
finally, (0(0+1)*0) + (1(0+1)*1) matches all binary strings which start and end with same symbol.