Discrete math

Anonymous
account_balance_wallet \$10

Question description

1. Consider:         x N , y N , x > y.

a) Translate the statement into an English sentence that contains no mathematical notation.

b) Find the negation of the statement in symbols.

c) State that the original sentence is true or false and prove your assertion by either (pretty) proving the original statement is true or by (pretty) proving the negation of the original statement is true.

2.      Let A, B, and C be sets. Prove       A x (BC) = (A x B ) ( A x C) using a set containment both directions argument.

3. Consider the relation R on the set S = 2z, the power set of Z , defined by ARB provided A ∩ B ≠ .   Which of the five properties: reflexive, irreflexive, symmetric, antisymmetric, transitive, does R have? Give a “pretty proof” for each of your answers.

Hints:

1. Think carefully about N being here as opposed to Z .

2. Think about what a typical element of A × (BC) “looks like”. Be sure to set up and write a set containment both directions argument the framework for which can be found as ex. 3 on the Day 18 notes. BUT a typical element of A × (BC) should not be called x.

Carnegie Mellon University

flag Report DMCA
Review

Anonymous
Top quality work from this guy! I'll be back!

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors