Discrete Mathematics Answers

cnf of q^(-q->(p^(-p->r)))

1.     Express the following system specifications using logical connectives:                                     

“The message is scanned for viruses whenever the message was sent from an   unknown system.”

“The message was sent from an unknown system but it was not scanned from viruses.”

“Access is granted whenever the user has paid the subscription fee and enters a valid password.”

“If the user has not entered a valid password but has paid the subscription fee, then access is granted.”

“You get an A in this class, but you do not do every exercise in this book.”

Find the general solution of the recurrence relation:

 an = an-1 + 2an-2 ,  with a0 = 2 and a1 = 7.

In a class of 35 students it is known that 24 of them do arts, 20 do chemistry and 22 do biology. All the students do at least one of the 3 subjects, 3 do all the three subjects while 7 do art and biology. 6 do art and chemistry but not biology and 8 do chemistry and biology. How many of them do chemistry or biology only or arts only?

Let P (x): x²/2 =x

find the following and identify their truth values

1. (P) 1

2. (P) 2

3.∀n, P(n)

4.∃n, P(n)

How many bit strings of length 14 contains the following types

(I) atmost three is?

(ii) an equal number of 0s and 1s

(iii) an odd number of 1s

Translate these statements into English sentence, where C(x) is "x is a comedian" and F(x) is "x is funny" and the domain consist of all people. a) Ax(C(x) -> F(x)) b) Ex(C(x) ^ F(x)) c) Ex(C(x) -> F(x))

P(n): n! > 3n for n ≥ 7. What is the Base Step?

Let f: Z®Z be such that f(x) = x +1.

Is f invertible? and if it is, what is its inverse?

Suppose R(x,y) is the predicate “x understands y,” the universe of discourse for x is the set of students in Discrete Class, and the universe of discourse for y is the set of examples in these lecture notes. 

Translate the following into English:

∃x∀yR(x,y)