Discrete Mathematics Answers

For each k ≥ 2 give an example of a graph with δ = k which contains no cycle of length greater than K+1?!.

From an initial position on the left bank of a river, a boatman is to transport a wolf, a goat and a
cabbage to the right bank of the river. His boat is only big enough to hold himself and one other object at a time. The wolf cannot be left alone with the goat, and the goat cannot be left alone with the cabbage. How should the boatman proceed? Describe a graph that can be used to solve the puzzle, and find a solution.

find the coefficient of x^3 y^3 in the expansion of (x+y)^n

Use a truth table to determine whether the argument given below is valid:
If it is a wild animal, it is dangerous. If it is dangerous, it will hurt
you. However, it is not dangerous. Therefore, it is not a wild animal.

Prove that for every set S, Ø \subseteq S.
Hint: Use vacuous proof.

Let A={x|x is even},B= 1 ,2,3,......,99,100},C={3,5,7,9} D={101,102} and E={101,103,105}.which of these sets can equal S if SA and S and B are disjoint? a.)A,b.)B,c.)C,d.)D,e.)E

Let a={2,{4,5},4}.which statement is correct? A.) 5 is an element of b,B.) {5} is an element of A C.) {4,5} is an element in A D.) {5} is a subset of A

In a primary school , the parents were asked about the number of hours they spend per day in helping their chaildren do their homework . there were 90 parents who helped for 1 and a half or half hour.50% did not help , 20% helped more 1 and a half hour and 30% helped for half hour to 1 and half hour .
how many parents were surveyed ?
how many said they did not help ?
how many said they did not helped for more than 1 and a half ?

In how many ways can one distribute ten distinct prizes among four students with exactly two students getting nothing?

How many ways have at least two students getting nothing?