# Finding a finite automata that accepts a language that is the combination of two other languages with their own automata

I’m told that we have two DFA one A and one B both on alphabet $$\sum$$.

I’m then told to define a DFA (5-tuple representation) with this condition {w | w = $$a_i b_i$$$$a_k b_k$$ and all the $$a \in A$$ and all the $$b \in B$$}

Also 1 $$\leq$$ i $$\leq$$ k and $$a_i \in \sum$$ and $$b_i \in \sum$$.

However I simply do not understand how I’m supposed to do this. Simply put my confusion is what $$w = a_i b_i$$ mean. Is it concatenation? Does it mean that the word $$w$$ is the concatenation of a with b?