Question

Let ∑= {a, b, …. z} and A = {Hello, World}, B= {Input, Output}, then (A*∩B) U (B*∩A) can be represented as:

(a) {Hello, World, Input, Output, ε}

(b) {Hello, World, ε}

(c) {Input, Output, ε}

(d) {}

I got this question in homework.

My query is from DFA Processing Strings topic in portion Finite Automata of Automata Theory

Answer 1

Right answer is (d) {}

Easiest explanation: Union operation creates the universal set by combining all the elements of first and second set while intersection operation creates a set of common elements of the first and the second state.