Discrete Mathematics Answers

Consider the following functions and determine if they are bijective. [A function is said to be bijective or bijection, if a function f : A → B is both one-to-one and onto.]

f : R × R → R, f(n, m) = 2m − n

Construct a truth table for each of these compound statements."( p \\leftrightarrow" q) "\\to(\\lnot p \\leftrightarrow q )"

Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all real numbers.

a) ∀x(x2 ( x)

b) ∀x(x2 ( 2)

c) ∀x(|x| > 0

In the given picture are three men: Neil Armstrong, Michael Collins and Buzz

Aldrin. They were on the Apollo 11 that set the first man on the moon in 1969.

Neil Armstrong was the first man walking on the moon. Which is an example of

an ordinal number?

(2)

A. Three

B. 11 (as in Apollo 11)

C. First

D. 1969

E. None of the above

2. Use set builder notation to give a description of each of these sets. a) {0, 3, 6, 9, 12} b) {−3, −2, −1, 0, 1, 2, 3} c) {m, n, o, p}

Let S = {Barnsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka Swallows, Witbank Aces, Royal Tigers, Dundee United, Lyon} be a universal set, A = {Southend, Liverpool, Maroka Swallows, Royal Tigers}, and B = {Barnsley, Manchester United, Southend}. Find n((A ∩ B)').

Thanks..

Consider the following functions and determine if they are bijective. [A function is said to be bijective or bijection, if a function f: A→B is both one-to-one and onto.]

(a) f: Z × Z→Z, f(n, m) = n² + m²

(b) f: R→R, f(x) = x³ − 3

(c) f: R × R→R, f(n, m) = 2m − n

Give an example of two uncountable sets A and B with a nonempty intersection, such that A−B is

(a) Finite

(b) Countably infinite

(c) Uncountably infinite