Make a DFA for the following with alphabet = {a,b} (do both state machine and formal description)

L1 = {w | w has an even number of as}

L2 = {w | w has substring aba}

L3 = {w | w has at least 3 as}

Construct the following DFAs using the algorithm

L1 intersect L2

L1 union L2

L2 intersect L3

L2 union L3