Discrete error-prone title

1. Let R be a set of real numbers, the mapping f: R → R, f (x) = $x^2$ , then f is ().

• Neither injective nor surjective.

2.R∘R = R R relationship is necessary and sufficient conditions on the set A is transmitted. ✘

• It is a sufficient condition. Because you can not transfer basis.

3.{a}⊆{{a}} ✘

4. If no simple vertices n = n-1, G is the number of edges in graph G e must be a tree. ✘

• It can not communicate, it is not a tree

Without there are n nodes in the connectivity graph G, n-1 edges, then G is a tree ✔

5. In the graph G of order n, when the presence of from node u v (u ≠ v) path from u to present the path length is less than or equal to n-1, v. ✔

6. The set S = {0,1}, * is the ordinary multiplication, the <S, *> that?

• Just monoid, but not group

7. All nonisomorphic 5-order root of the tree have?

• 9

All non-homogeneous rooted tree with a fourth-order trees.

• 4

9. regular height h of at least 2 ____ tree leaves.

• h+1

10. On supremum $\Leftrightarrow$ least upper bound
infimum $\Leftrightarrow$ greatest lower bound

11. The set A = {1, 2, 3}, then there is () a binary relation on A

• $2^{3^2}$

12. The cyclic group is Abelian group, but not necessarily cyclic group Abelian group.

13. A necessary and sufficient condition has no spanning a directed graph is that it is communicating FIG.

14. The collection {0} power set that?

• {Φ, {0}} Note: power set is set.

15. FIG communication must strongly connected graph is one way, one-way communication must be weak FIG communication FIG. Not vice versa.

16. collection $A$ = {l, 2,3}. The collection $A$ equivalence relation on a few?

• 5

17. The set S = {a, b}, then the relationship R S = {<a, b>, <b, c>, <a, c>} is transmitted. ✘

18. official $A$ = $\exist$ x (F(x) $\rightarrow$ (X, Y)) to explain G $I$ : individual field D = N, F (x)is $A$ true value?

• Note: Here $\exist$ scope of x is more than the antecedent, it is not directly generations. This question is meant that x exists if x> 3 then the x = y holds. Because there is no value of y, so this question of the true value can not be determined.

19. set $S$ = {l, 2,3}, defined $S$ x $S$ equivalence relation on $R$ = {<<a,b> , <c,d>>|a + d = b + c} , 则 $R$ number of equivalence class is?

20. The cyclic group $G$ = <A> subgroup of the cyclic group remains
when $G$ is a group of infinite loop, the $G$ sub-groups except that {e} is an infinite cyclic group.

Analytical:
X and -x is automorphism.

Because the two-shot is not satisfied 2x, x + 5 is not satisfied endomorphism: f (x + y) = f (x) + f (y).

Parsing: D

Note:
The fourth map is a simple graph.

23.A = {a, b}, A of the power set P (A) to have its own two-shot of ____

Analysis: 24

There are four power set, 4x3x2 = 24