Question

How would you find four elements from the set:
S1 ∩ S2 where S1 = {(0)^∗ (01)^∗ (101)^i 0^∗|i ≥ 0} and S2 = {1^i 0^i 1(10)^(i+1)|i ≥ 0}

Answer 1

I've gotten S1 as being {∈,0,00,000,..}{∈,01,0101,...} ∈ {∈,0,00,000,...} for all i >= 0 and S2 as being {(∈ ∈ 1 10},{1 0 1 1010}...} but I'm not sure how to find the intersection of the two.