***Please help me correct my answers for this practice test for my discrete math class. My answers are in bold.

1. True/False:{3} {1,2,3}.
2. True/False:3 {1,2,3}.
3. True/False:1 {1,2,3}.
4. True/False:{1} {1,2,3}.
5. True/False: {{a, b},{b}, c}.
6. True/False: .
7. True/False{1,2,3} {2,3,4}={2,3}.
8. True/False{a, b, c} {b, c, d}={a}.
9. True/False{2,3} {2,3,4}={(2,2),(2,3),(3,2),(3,3),(4,2),(4,3)}.

Consider the following relations on the setS={2,3,4,5,6}.

10. True/False{(2,2),(3,3),(4,4),(5,5)}is symmetric.

11. True/False{(2,2),(3,3),(4,4),(5,5)}is reflexive.

12. True/False{(2,2),(3,3),(4,4),(5,5)}is a function onS

13. True/False{(2,2),(3,3),(4,4),(5,5)}is transitive.

14. g:ZZis defined by the formulag(x) = 2x+ 1. Select the correct option:

(a)ghas inverseg1(x) = (x1)/2.

(b)ghas inverseg1(x) =x/21.

(c)gdoes not have an inverse because it is not injective.

(d) None of the above.

15. Suppose the functionf:R0Ris given by the formulaf(x) =x21. Select the correct option:

(a)fis a bijection.

(b)fis injective but not surjective.

(c)fis not injective but is surjective.

(d)fis neither injective nor surjective.

16. There is a graph with with9vertices of degrees:4,4,5,6,6,7,8,8,10. (a) The graph has an Euler Circuit, but not an Euler Path.

(b) The graph has an Euler Path, but not an Euler Circuit.

(c) The graph has neither an Euler Path, nor an Euler Circuit.

(d) The graph has both an Euler Path and an Euler Circuit.

17. The graph in the previous question has:

(a)29edges.

(b)30edges.

(c)31edges.

(d)116edges.

(e) There is not enough information to determine the number of edges.

18.Compute[19]₇³²¹. Select the correct answer:

(a)[0]₇

(b)[1]₇

(c)[2]₇

(d)[3]₇

(e)[4]₇

(f)[5]₇

(g)[6]₇

19.True/False1213 (mod 5).

20.The depth-first search algorithm has been applied to a connected graph with no bridges which has2000vertices and6000edges. After the labeling directions are assigned to the edges to make the graph strongly connected. The resulting directed graph must has:

(a)3999back edges.

(b)4000back edges.

(c)4001back edges.

(d)4002back edges.

(e) The number of back edges cannot be determined from the given information.