The congruence modulo 3 relation, T , is defined from Z to Z as follows: For all
Chapter 8, Problem 3(choose chapter or problem)
The congruence modulo 3 relation, T , is defined from Z to Z as follows: For all integers m and n,
m T n \(\Leftrightarrow\) 3 | (m − n).
a. Is 10 T 1? Is 1 T 10? Is (2, 2) \(\in\) T? Is (8, 1) \(\in\) T ?
b. List five integers n such that n T 0.
c. List five integers n such that n T 1.
d. List five integers n such that n T 2.
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.
Text Transcription:
Leftrightarrow
in
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