Discrete Mathematics Answers

Find the solution of the recurrence relation

an = 4an−1 − 3an−2 + 2

n + n + 3 , a0 = 1 and a1 = 4

State whether the null hypothesis should be rejected on the basis of given P-value. P-value 0.002, a 0.01, one-tailed test.

Determine whether each of these functions from {a,b,c,d} to itself is one-to-one. a) f(a)=b, f(b)=a, f(c)=c, f(d)=d

If the truth value of p is "false", the truth value of q is "false", and the truth value of r is "true", which of the following expressions is "false"?

There are 21 pupils in a grade 7 class. The class teacher has to choose eight of the pupils for a group that will visit Germany in three months time. In how many different ways can the teacher select pupils for the group ?

Let A = {x ∈ R : x 2 = 2} and B = {x ∈ R : x ≥ 0}.

1. Find A ∩ B.

2. Find A ∪ B.

3. Find A − B.

4. For U = R, find Ac and Bc .

5. Find N − B.

Let A = {2, 3, 5, 7, 11, 13} and B = {A, 2, 11, 18}.

1. Find A ∪ B. 2. Find A ∩ B. 3. Find A − B.

Let a and b be two cardinal numbers. Modify Cantor’s definition of a < b to define a ≤ b. (Hint: Examine what happens if you drop condition (a) from Cantor’s definition of a < b.) 2. Prove that a ≤ a. 3. Prove that if a ≤ b and b ≤ c, then a ≤ c. 4. Do you think that a ≤ b and b ≤ a imply

a = b? Explain your reasoning. (Hint: This is not as trivial as it might look.)

1.                  Let p and q be the propositions “Swimming at the Corregidor Island shore is allowed” and “Sharks have been spotted near the shore,” respectively. Express each of these compound propositions as an English sentence. 

Three persons enter into car, where there are 5 seats. In how many ways can

they take up their seats?