Discrete Mathematics Answers

Given an example of a tree of order 6 containing four vertices of degree 1 and two vertices of degree 3.

• Determine whether each of the following statements is a proposition or not. If it is, give its truth value.p: Mindanao is an island in the Philippines. 
• q: Find a number which divides your age. 
• r: My seatmate will get a perfect score in the Logic exam.
• s: Welcome to the Philippines!

13.Solve the recurrence relation using generating function , a_n-9a_n-1+20a_n-2=0 for n greater than or equals to 2 with initial values a₀=-3, a₁=-10.

12. Solve the recurrence relation a_n=a_n-1+n²,where a₀=7 by substitution

11. For arbitrary constants c₁,c₂, And c₃ show that a_n=c₁2ⁿ+c₂5ⁿ+c₃n5ⁿ satisfies the recurrence relations a_n-12a_n-1+45a_n-2-50a_n-3=0

8. Find a generating function for the sequence (a₀, a₁,....a_r.....), where ar=the number of non negative integral solutions to e₁+e₂ +....e_n=r where 0 less than or equal to e₁ less than or equal to 1 for each i=1,2,3,.....n

What is the truth value of Ex P(×),where P(×) is the statement "x² >12" and the universe of discourse consists of the negative integers not exceeding 4?

What is the domain of the function is this proposition?

Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find

a. (A ∪ B) ∩ C.

b. (A ∩ B) ∪ C.

c. (A ∪ B) ∩ (A ∪ C).

Identify if the given statement is a proposition or not.

There are no black flies in Maine.