True or False (my answers in parenthesis) 1) An Eulerian trail is the same as an

Question

True or False (my answers in parenthesis)

1) An Eulerian trail is the same as an Eulerian circuit. (?)

2) Given the three statements P(1), P(2), P(3) with P(1) implies P(2), P(2) implies P(3), and you are also given that P(1) is true, P(3) can be false. (True)

3) The number of all functions from an n-set to a 2-set is 2^n. (?)

4) There is a tree with 6 vertices and such that the degree of every vertex is greater than 1. (True)

5) If there is a cycle in a graph, then this graph cannot be a tree. (True)

6) The number of onto functions from the set {a, b, c, d, e, f} onto {1, 2, 3} is 0. (True)

7) The set of the sequence of numbers S(i), i = 1, 2, ... defined recursively by:

(a) S(1) = 7

(b) S(n) = 3 ∗ S(n − 1) + 2 for n >= 2

contains the number 215. (?)

8) If you can show q by assuming p, then you can conclude p implies q is true. (?)

9) If f is Theta(g), then beyond some point on the right hand coordinate axis, f(x) must fall between 1/2 g(x) and 2g(x). (?)

10) Given T(n) = T(n − 1) + 1. Then T(n) = O(n). (?)

Explanation / Answer

1.true

2.true

3.false

4.true

5.true

6.true

7.false

8.true

9.false

10.true

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