几道简单的离散数学 但是是英语的 求学霸帮忙 作对有追分

几道简单的离散数学 但是是英语的 求学霸帮忙 作对有追分
一、Let S={{1,2,3},{4,5},{6,7,8}} Determine which of the following claims is true and which is false.
(a) 1 属于 S
(b){1,2,3}⊆S
(c){6,7,8} 属于 S
(d){{4,5}}⊆S
(e)空集 不属于 S
(f)空集⊆S
(g){{1,2,3},{6,7,8}}⊆S
(h){{2,3},{4,5}}⊆S
二、Let R be a binary relation on the set of integers defined as follows:
xRy means that the sum s+y is dibided bu 3. Is this relation transitive?
三、Consider a family with fibe children A,B,C,D,E where A and D are girls, and B,C and E are boys.Let R be the brother-sister relation on the set of children {A,B,C,D,E} defined as follows:"xRy" means that x is a brother of y and y is a sister of x.
Then R={(B,A),(B,D),(C,A),(C,D),(E,A),(E,D)}.
Specify analogously the following relations on {A,B,C,D,E}:
(a)The sister-brother relation
(b)The brother-brother relation
(c)The sister-sister relation
(d)Draw directed graphs representing the brother-sister relation and sister-brother relation.
四、How many edges are there in a simple graph whith 10 nodes each pf degree 4?
五、Does there exist a simple graph which has 5 nodes and each of its nodes has degree 3?
六、What is the number of edges in the complete simple graph on 7 nodes?