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.

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