Discrete Mathematics Answers

The chairs of an auditorium are to be labeled with an uppercase English letter followed by a positive integer not exceeding 100. What is the largest number of chairs that can be labeled differently?

∀n ≥ 1, Xn i=1 i(i!) = (n + 1)! − 1

A function f is said to be one-to-one, or an injection, if and only if f(a) = f(b) implies that a = b for all a and b in the domain of f. Note that a function f is one-to-one if and only if f(a) ≠ f(b) whenever a ≠ b. This way of expressing that f is one-to-one is obtained by taking the contrapositive of the implication in the definition. A function f from A to B is called onto, or a surjection, if and only if for every element b ∈ B there is an element a ∈ A with f(a) = b. A function f is onto if ∀y∃x( f(x) = y), where the domain for x is the domain of the function and the domain for y is the codomain of the function

Now consider that f is a function from A to B, where A and B are finite sets with |A| = |B|. Show that f is one-to-one if and only if it is onto.

A function f is said to be one-to-one, or an injection, if and only if f(a) = f(b) implies that a = b for all a and b in the domain of f. Note that a function f is one-to-one if and only if f(a) ≠ f(b) whenever a ≠ b. This way of expressing that f is one-to-one is obtained by taking the contrapositive of the implication in the definition. A function f from A to B is called onto, or a surjection, if and only if for every element b ∈ B there is an element a ∈ A with f(a) = b. A function f is onto if ∀y∃x( f(x) = y), where the domain for x is the domain of the function and the domain for y is the codomain of the function

Now consider that f is a function from A to B, where A and B are finite sets with |A| = |B|. Show that f is one-to-one if and only if it is onto.

Greatest and smallest elements of poset 2,4,5,10,12,20,25

Prove by mathematical induction. 1 + 5 + 9 +...+ (4n-3) = (2n+1)(n-1) for n ≥ 2

Find the number of positive integers less than 601 that are not divisible by 4 or 5 or 6

In a company, there are 50 employees and some committees. If each employee belongs

to 6 committees and each committee consists of 10 people, how many committees are there?

Find a common domain for the variables x, y, z, and w for which the statement ∀x∀y∀z∃w((w ≠ x) ∧ (w ≠ y) ∧ (w ≠ z)) is true and another common domain for these variables for which it is false

. Consider the functions from the set of students in a discrete mathematics class. Under what

conditions is the function one-to-one if it assigns to a student his or her a) mobile phone

number. b) student identification number. c) final grade in the class. d) home town