Discrete Mathematics Answers

how many 2-digit or 3-digits numbers can be formed using the digits 1,2,3,4,5,6,8 and 9 if no repetition is allowed ?

how many possible telephone numbers are there when there are seven digits the first two of which between 2 and 9 inclusive the third digit between 1 and 9 inclusive and each of the remaining may be between 0 and 9 inclusive ?

 How many three digit numbers can be formed using the digits 1,2,3,4,5,6,7,8 and 9?

1)    Translate the given statement into propositional logic using the propositions provided

You cannot edit a protected Wikipedia entry unless you are an administrator. Express your answer in terms of e: “You can edit a protected Wikipedia entry” and a: “You are an administrator.

List all the ordered Paris in the relation R=[(a, b) |a divides b ] on the set {1,2,3,4,5,6}.

Let P(x) be the statement “x spends more than five hours every weekday in class,” where the

domain for x consists of all students. Express each of these quantifications in English.

a) ∃𝑥𝑃(𝑥)

b) ∀𝑥𝑃(𝑥)

c) ∃𝑥¬𝑃(𝑥)

d) ∀𝑥¬𝑃(𝑥)

|4| >2 if -2 <1<2

Show that (¬𝑃 ⟶ 𝑅) ∧ (𝑄 ↔ 𝑃) ⟺ (𝑃 ∨ 𝑄 ∨ 𝑅) ∧ (𝑃 ∨ ¬𝑄 ∨ 𝑅) ∧ (𝑃 ∨ ¬𝑄 ∨ ¬𝑅) ∧ (¬𝑃 ∨ 𝑄 ∨ 𝑅) ∧ (¬𝑃 ∨ 𝑄 ∨ ¬𝑅).

Prove that 1·1 ! + 2·2!+· ··+ n · n! = (n+I)!-1

whenever n is a positive integer.