04 Aug We describe the functions f:X→Y and g:X→Y
Homework 8 1.
Let X be the set {1,2,3,4,5} and Y be the set {6,7,8,9,10}.We describe the functions f:X→Y and g:X→Y in the following tables. Answer each part and give a reason for each negative answer.
n | f(n) n | g(n）
1|6 1|10
2|7 2|9
3|6 3|8
4|7 4|7
5|6 5|6
a. Is f one-to-one?
b. Is f onto?
c. Is f a correspondence?
d. Is g one-to-one?
e. Is g onto?
f.I s g a correspondence?
2.Answer all parts for the following DFA M and give reasons for your answers.
1
1 0
0,1
a. Is(M,0100)E ADFA?
b.Is(M,011)E ADFA?
c.Is(M)E ADFA?
d. Is(M,0100)E AREx?
e.Is(M)E EDFA?
f.Is(M,M)E EQDFA 3.|
Let INFINITE DFA={(A)| A is a DFA and L(A) is an infinite language}.Show that INFINTTEDFA is decidable.
4.
Let A={(M)| M is a DFA that doesn’t accept any string containing an odd number of 1s}.Show that A is decidable.
