Discrete Mathematics Answers

Show that the relation p = {(a,b) | a -b is an integer} on the set of real numbers R is equivalence relation

i)                  Which type of relation is shown in below expression

R1 = { (a,b) | a = b } 

Find each of the function below, indicate whether the function in onto, on-to-one neither or both. If the function is not onto or nor one-to-one, give an example showing why

G;R      R. g(x)=x^3

1. A debating team consists of three boys and two girls. Find the number n of ways they can sit in a row if the boys and girls are each to sit together.

Prove the following statement by induction. For all nonnegative integers nn, 3 divides n^3 +2n +3n. State the mathematical induction and show your work clearly. 

An examination paper consists of 5 questions in section A and 5 questions in section B. A total of 8 questions must be answered. In how many ways can a student select the questions if he is to answer at least 4 questions from section A.

Find each of the function below, indicate whether the function in onto, on-to-one neither or both. If the function is not onto or nor one-to-one, give an example showing why

                               .           

H;Z     Z. h(x)=x^3

Find each of the function below, indicate whether the function in onto, on-to-one neither or both. If the function is not onto or nor one-to-one, give an example showing why

                            .           

G;R     R. g(x)=x^3

i)                  Which type of relation is shown in below expression

R1 = { (a,b) | a = b } 

25. Solve recurrence relation an+3=3an+2+4an+1-12an for n20 with a0-0,al--11,a2--15