4.2 (c) {1, 3, 4, 5}

4.10 (d)

State	Input	Next State	|	State	Input	Next State
1	a	2	|	1,4,5	b	empty set
1	b	empty set	|	1,2,5	a	1,2
2	a	empty set	|	1,2,5	b	3
2	b	3	|	1,2	a	2
3	a	1,4,5	|	1,2	b	3
3	b	empty set	|	empty set	a	empty set
1,4,5	a	1,2,5	|	empty set	b	empty set

Every state of DFA that contains state 1 of NFA is an accepting state.

4.13 Yes for (a) and (c) and No for (b).

4.14 or
        aa^*b^*(a + b)( a + ba^*b^*(a + b) )^* or anything equivalent.

4.16 (c)
(e)

3. The set of states, the alphabet and the initial state of the NFA are the same as those o f the ,
The set of accepting states of the NFA is equal to the set of accepting states of the (denote it by A), if no accepting state can be reached from the initial state by -arcs in the , else = .
For a transition of the NFA, collect all the states reachable from q by taking any number of -arcs, then one a-arc, then any number of -arcs.