Consider:∀ x ∈ N , ∃ y ∈ N , x > y.
What are the four phases of the business cycle?
September 20, 2019Jun is a math major but not a computer science major.
September 20, 2019Consider:∀ x ∈ N , ∃ y ∈ N , x > y.
Question Description
- 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.
- Let A, B, and C be sets. Prove A x (B∪C) = (A x B ) ∪ ( A x C) using a set containment both directions argument.
- Consider the relationRon 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:
- Think carefully aboutNbeing here as opposed to Z .
- Think about what a typical element of A × (B∪C) “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 × (B∪C) should not be called x.
