Consider the DFAs M and N given above. The number of states in a minimal DFA that accepts the language L(M) ∩ L(N) is____________________

Consider DFA M,

It is accepting all the string that ends with a.

Language for DFA M L(M) = {a, aa, ba, aaa, aba, …}

Regular expression = (a + b )*a

DFA N is accepting all the languages ending with b.

Language for DFA N L (n) = {b, ab, bb, aab, abb, bbb,…….}

Regular expression = (a + b)*b

Intersection of both these languages L (M) ꓵ L(N) = { } = Ø i.e. empty language

For this, we just need 1 state with all transitions to itself and no final state.