Math Solutions

[Step-by-Step] The congruence modulo 3 relation, T, is defined from Z to Z as follows: For all integers m and n, m T n => 3 \mid(m-n). Is $10 T 1 ?$ Is $1

Question: The congruence modulo 3 relation, \(T\), is defined from \(\mathbf{Z}\) to \(\mathbf{Z}\) as follows:

For all integers \(m\) and \(n, \quad m T n \Leftrightarrow 3 \mid(m-n)\).

  1. Is $10 T 1 ?$ Is $1 T 10 ?$ Is \((2,2) \in T ?\) Is \((8,1) \in T ?\)
  2. List five integers \(n\) such that $n T 0$.
  3. List five integers \(n\) such that $n T 1$.
  4. List five integers \(n\) such that $n T 2$.
    \(H\) e. Make and prove a conjecture about which integers are related by \(T\) to 0, which integers are related by \(T\) to 1 , and which integers are related by \(T\) to 2 .
    Price: $2.99
    Solution: The downloadable solution consists of 2 pages
    Deliverable: Word Document


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